1.13: Difference between revisions

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{{DISPLAYTITLE:Algebraic and Analytic Methods - 1.13 Differential Equations}}
<div style="width: 100%; height: 75vh; overflow: auto;">
<div style="width: 100%; height: 75vh; overflow: auto;">
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! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/1.13.E2 1.13.E2] || [[Item:Q463|<math>w(z) = Aw_{1}(z)+Bw_{2}(z)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w(z) = Aw_{1}(z)+Bw_{2}(z)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w(z) = Aw[1](z)+ Bw[2](z)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w[z] == Subscript[Aw, 1][z]+ Subscript[Bw, 2][z]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/1.13.E2 1.13.E2] || <math qid="Q463">w(z) = Aw_{1}(z)+Bw_{2}(z)</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w(z) = Aw_{1}(z)+Bw_{2}(z)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w(z) = Aw[1](z)+ Bw[2](z)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w[z] == Subscript[Aw, 1][z]+ Subscript[Bw, 2][z]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/1.13#Ex1 1.13#Ex1] || [[Item:Q464|<math>w_{1}(z_{0}) = 1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w_{1}(z_{0}) = 1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w[1](z[0]) = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[w, 1][Subscript[z, 0]] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/1.13#Ex1 1.13#Ex1] || <math qid="Q464">w_{1}(z_{0}) = 1</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w_{1}(z_{0}) = 1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w[1](z[0]) = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[w, 1][Subscript[z, 0]] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/1.13#Ex3 1.13#Ex3] || [[Item:Q466|<math>w_{2}(z_{0}) = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w_{2}(z_{0}) = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w[2](z[0]) = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[w, 2][Subscript[z, 0]] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/1.13#Ex3 1.13#Ex3] || <math qid="Q466">w_{2}(z_{0}) = 0</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w_{2}(z_{0}) = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w[2](z[0]) = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[w, 2][Subscript[z, 0]] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/1.13.E6 1.13.E6] || [[Item:Q470|<math>Aw_{1}(z)+Bw_{2}(z) = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>Aw_{1}(z)+Bw_{2}(z) = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Aw[1](z)+ Bw[2](z) = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[Aw, 1][z]+ Subscript[Bw, 2][z] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/1.13.E6 1.13.E6] || <math qid="Q470">Aw_{1}(z)+Bw_{2}(z) = 0</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>Aw_{1}(z)+Bw_{2}(z) = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Aw[1](z)+ Bw[2](z) = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[Aw, 1][z]+ Subscript[Bw, 2][z] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/1.13.E9 1.13.E9] || [[Item:Q473|<math>w(z) = w_{0}(z)+Aw_{1}(z)+Bw_{2}(z)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w(z) = w_{0}(z)+Aw_{1}(z)+Bw_{2}(z)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w(z) = w[0](z)+ Aw[1](z)+ Bw[2](z)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w[z] == Subscript[w, 0][z]+ Subscript[Aw, 1][z]+ Subscript[Bw, 2][z]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/1.13.E9 1.13.E9] || <math qid="Q473">w(z) = w_{0}(z)+Aw_{1}(z)+Bw_{2}(z)</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w(z) = w_{0}(z)+Aw_{1}(z)+Bw_{2}(z)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w(z) = w[0](z)+ Aw[1](z)+ Bw[2](z)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w[z] == Subscript[w, 0][z]+ Subscript[Aw, 1][z]+ Subscript[Bw, 2][z]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-  
|-  
| [https://dlmf.nist.gov/1.13.E10 1.13.E10] || [[Item:Q474|<math>w_{0}(z) = w_{2}(z)\int\frac{w_{1}(z)r(z)}{\Wronskian@{w_{1}(z),w_{2}(z)}}\diff{z}-w_{1}(z)\int\frac{w_{2}(z)r(z)}{\Wronskian@{w_{1}(z),w_{2}(z)}}\diff{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w_{0}(z) = w_{2}(z)\int\frac{w_{1}(z)r(z)}{\Wronskian@{w_{1}(z),w_{2}(z)}}\diff{z}-w_{1}(z)\int\frac{w_{2}(z)r(z)}{\Wronskian@{w_{1}(z),w_{2}(z)}}\diff{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>w[0](z) = w[2](z)* int((w[1](z)* r(z))/((w[1](z))*diff(w[2](z), z)-diff(w[1](z), z)*(w[2](z))), z)- w[1](z)* int((w[2](z)* r(z))/((w[1](z))*diff(w[2](z), z)-diff(w[1](z), z)*(w[2](z))), z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[w, 0][z] == Subscript[w, 2][z]* Integrate[Divide[Subscript[w, 1][z]* r[z],Wronskian[{Subscript[w, 1][z], Subscript[w, 2][z]}, z]], z, GenerateConditions->None]- Subscript[w, 1][z]* Integrate[Divide[Subscript[w, 2][z]* r[z],Wronskian[{Subscript[w, 1][z], Subscript[w, 2][z]}, z]], z, GenerateConditions->None]</syntaxhighlight> || Translation Error || Translation Error || - || -
| [https://dlmf.nist.gov/1.13.E10 1.13.E10] || <math qid="Q474">w_{0}(z) = w_{2}(z)\int\frac{w_{1}(z)r(z)}{\Wronskian@{w_{1}(z),w_{2}(z)}}\diff{z}-w_{1}(z)\int\frac{w_{2}(z)r(z)}{\Wronskian@{w_{1}(z),w_{2}(z)}}\diff{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w_{0}(z) = w_{2}(z)\int\frac{w_{1}(z)r(z)}{\Wronskian@{w_{1}(z),w_{2}(z)}}\diff{z}-w_{1}(z)\int\frac{w_{2}(z)r(z)}{\Wronskian@{w_{1}(z),w_{2}(z)}}\diff{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>w[0](z) = w[2](z)* int((w[1](z)* r(z))/((w[1](z))*diff(w[2](z), z)-diff(w[1](z), z)*(w[2](z))), z)- w[1](z)* int((w[2](z)* r(z))/((w[1](z))*diff(w[2](z), z)-diff(w[1](z), z)*(w[2](z))), z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[w, 0][z] == Subscript[w, 2][z]* Integrate[Divide[Subscript[w, 1][z]* r[z],Wronskian[{Subscript[w, 1][z], Subscript[w, 2][z]}, z]], z, GenerateConditions->None]- Subscript[w, 1][z]* Integrate[Divide[Subscript[w, 2][z]* r[z],Wronskian[{Subscript[w, 1][z], Subscript[w, 2][z]}, z]], z, GenerateConditions->None]</syntaxhighlight> || Translation Error || Translation Error || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/1.13#Ex5 1.13#Ex5] || [[Item:Q476|<math>W(\xi) = w\left(\frac{1}{\xi}\right)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>W(\xi) = w\left(\frac{1}{\xi}\right)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">W(xi) = w((1)/(xi))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">W[\[Xi]] == w[Divide[1,\[Xi]]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/1.13#Ex5 1.13#Ex5] || <math qid="Q476">W(\xi) = w\left(\frac{1}{\xi}\right)</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>W(\xi) = w\left(\frac{1}{\xi}\right)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">W(xi) = w((1)/(xi))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">W[\[Xi]] == w[Divide[1,\[Xi]]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-  
|-  
| [https://dlmf.nist.gov/1.13#Ex8 1.13#Ex8] || [[Item:Q490|<math>\deriv[2]{U}{z}+IU = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv[2]{U}{z}+IU = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(U, [z$(2)])+ I*U = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[U, {z, 2}]+ I*U == 0</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .5000000004+.8660254040*I
| [https://dlmf.nist.gov/1.13#Ex8 1.13#Ex8] || <math qid="Q490">\deriv[2]{U}{z}+IU = 0</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv[2]{U}{z}+IU = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(U, [z$(2)])+ I*U = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[U, {z, 2}]+ I*U == 0</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .5000000004+.8660254040*I
Test Values: {I = 1/2*3^(1/2)+1/2*I, U = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .5000000004+.8660254040*I
Test Values: {I = 1/2*3^(1/2)+1/2*I, U = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .5000000004+.8660254040*I
Test Values: {I = 1/2*3^(1/2)+1/2*I, U = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .5000000004+.8660254040*I
Test Values: {I = 1/2*3^(1/2)+1/2*I, U = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .5000000004+.8660254040*I
Line 34: Line 36:
Test Values: {Rule[Complex[0, 1], 2], Rule[U, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
Test Values: {Rule[Complex[0, 1], 2], Rule[U, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-  
|-  
| [https://dlmf.nist.gov/1.13#Ex9 1.13#Ex9] || [[Item:Q491|<math>\deriv[2]{V}{z}+JV = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv[2]{V}{z}+JV = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(V, [z$(2)])+ J*V = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[V, {z, 2}]+ J*V == 0</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .5000000004+.8660254040*I
| [https://dlmf.nist.gov/1.13#Ex9 1.13#Ex9] || <math qid="Q491">\deriv[2]{V}{z}+JV = 0</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv[2]{V}{z}+JV = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(V, [z$(2)])+ J*V = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[V, {z, 2}]+ J*V == 0</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .5000000004+.8660254040*I
Test Values: {J = 1/2*3^(1/2)+1/2*I, V = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .5000000004+.8660254040*I
Test Values: {J = 1/2*3^(1/2)+1/2*I, V = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .5000000004+.8660254040*I
Test Values: {J = 1/2*3^(1/2)+1/2*I, V = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .5000000004+.8660254040*I
Test Values: {J = 1/2*3^(1/2)+1/2*I, V = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .5000000004+.8660254040*I

Latest revision as of 11:00, 28 June 2021


DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
1.13.E2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w(z) = Aw_{1}(z)+Bw_{2}(z)}
w(z) = Aw_{1}(z)+Bw_{2}(z)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
w(z) = Aw[1](z)+ Bw[2](z)
 
w[z] == Subscript[Aw, 1][z]+ Subscript[Bw, 2][z]
 Skipped - no semantic math Skipped - no semantic math - -
1.13#Ex1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{1}(z_{0}) = 1}
w_{1}(z_{0}) = 1		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
w[1](z[0]) = 1
 
Subscript[w, 1][Subscript[z, 0]] == 1
 Skipped - no semantic math Skipped - no semantic math - -
1.13#Ex3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{2}(z_{0}) = 0}
w_{2}(z_{0}) = 0		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
w[2](z[0]) = 0
 
Subscript[w, 2][Subscript[z, 0]] == 0
 Skipped - no semantic math Skipped - no semantic math - -
1.13.E6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle Aw_{1}(z)+Bw_{2}(z) = 0}
Aw_{1}(z)+Bw_{2}(z) = 0		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
Aw[1](z)+ Bw[2](z) = 0
 
Subscript[Aw, 1][z]+ Subscript[Bw, 2][z] == 0
 Skipped - no semantic math Skipped - no semantic math - -
1.13.E9 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w(z) = w_{0}(z)+Aw_{1}(z)+Bw_{2}(z)}
w(z) = w_{0}(z)+Aw_{1}(z)+Bw_{2}(z)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
w(z) = w[0](z)+ Aw[1](z)+ Bw[2](z)
 
w[z] == Subscript[w, 0][z]+ Subscript[Aw, 1][z]+ Subscript[Bw, 2][z]
 Skipped - no semantic math Skipped - no semantic math - -
1.13.E10 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{0}(z) = w_{2}(z)\int\frac{w_{1}(z)r(z)}{\Wronskian@{w_{1}(z),w_{2}(z)}}\diff{z}-w_{1}(z)\int\frac{w_{2}(z)r(z)}{\Wronskian@{w_{1}(z),w_{2}(z)}}\diff{z}}
w_{0}(z) = w_{2}(z)\int\frac{w_{1}(z)r(z)}{\Wronskian@{w_{1}(z),w_{2}(z)}}\diff{z}-w_{1}(z)\int\frac{w_{2}(z)r(z)}{\Wronskian@{w_{1}(z),w_{2}(z)}}\diff{z}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
w[0](z) = w[2](z)* int((w[1](z)* r(z))/((w[1](z))*diff(w[2](z), z)-diff(w[1](z), z)*(w[2](z))), z)- w[1](z)* int((w[2](z)* r(z))/((w[1](z))*diff(w[2](z), z)-diff(w[1](z), z)*(w[2](z))), z)

Subscript[w, 0][z] == Subscript[w, 2][z]* Integrate[Divide[Subscript[w, 1][z]* r[z],Wronskian[{Subscript[w, 1][z], Subscript[w, 2][z]}, z]], z, GenerateConditions->None]- Subscript[w, 1][z]* Integrate[Divide[Subscript[w, 2][z]* r[z],Wronskian[{Subscript[w, 1][z], Subscript[w, 2][z]}, z]], z, GenerateConditions->None]
Translation Error Translation Error - -
1.13#Ex5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle W(\xi) = w\left(\frac{1}{\xi}\right)}
W(\xi) = w\left(\frac{1}{\xi}\right)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
W(xi) = w((1)/(xi))
 
W[\[Xi]] == w[Divide[1,\[Xi]]]
 Skipped - no semantic math Skipped - no semantic math - -
1.13#Ex8 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{U}{z}+IU = 0}
\deriv[2]{U}{z}+IU = 0		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
diff(U, [z$(2)])+ I*U = 0

D[U, {z, 2}]+ I*U == 0
Failure Failure
Failed [300 / 300]
Result: .5000000004+.8660254040*I
Test Values: {I = 1/2*3^(1/2)+1/2*I, U = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}


Result: .5000000004+.8660254040*I
Test Values: {I = 1/2*3^(1/2)+1/2*I, U = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}


Result: .5000000004+.8660254040*I
Test Values: {I = 1/2*3^(1/2)+1/2*I, U = 1/2*3^(1/2)+1/2*I, z = 1/2-1/2*I*3^(1/2)}


Result: .5000000004+.8660254040*I
Test Values: {I = 1/2*3^(1/2)+1/2*I, U = 1/2*3^(1/2)+1/2*I, z = -1/2*3^(1/2)-1/2*I}

... skip entries to safe data
Failed [210 / 210]
Result: Complex[0.8660254037844387, 0.49999999999999994]
Test Values: {Rule[Complex[0, 1], 1], Rule[U, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}


Result: Complex[1.7320508075688774, 0.9999999999999999]
Test Values: {Rule[Complex[0, 1], 2], Rule[U, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}

... skip entries to safe data
1.13#Ex9 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{V}{z}+JV = 0}
\deriv[2]{V}{z}+JV = 0		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
diff(V, [z$(2)])+ J*V = 0

D[V, {z, 2}]+ J*V == 0
Failure Failure
Failed [300 / 300]
Result: .5000000004+.8660254040*I
Test Values: {J = 1/2*3^(1/2)+1/2*I, V = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}


Result: .5000000004+.8660254040*I
Test Values: {J = 1/2*3^(1/2)+1/2*I, V = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}


Result: .5000000004+.8660254040*I
Test Values: {J = 1/2*3^(1/2)+1/2*I, V = 1/2*3^(1/2)+1/2*I, z = 1/2-1/2*I*3^(1/2)}


Result: .5000000004+.8660254040*I
Test Values: {J = 1/2*3^(1/2)+1/2*I, V = 1/2*3^(1/2)+1/2*I, z = -1/2*3^(1/2)-1/2*I}

... skip entries to safe data
Failed [300 / 300]
Result: Complex[0.5000000000000001, 0.8660254037844386]
Test Values: {Rule[J, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[V, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}


Result: Complex[0.5000000000000001, 0.8660254037844386]
Test Values: {Rule[J, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[V, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}

... skip entries to safe data
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