Algebraic and Analytic Methods - 1.13 Differential Equations

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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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