PainlevΓ© Transcendents - 32.13 Reductions of Partial Differential Equations

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DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
32.13.E1 v t - 6 ⁒ v 2 ⁒ v x + v x ⁒ x ⁒ x = 0 subscript 𝑣 𝑑 6 superscript 𝑣 2 subscript 𝑣 π‘₯ subscript 𝑣 π‘₯ π‘₯ π‘₯ 0 {\displaystyle{\displaystyle v_{t}-6v^{2}v_{x}+v_{xxx}=0}}
v_{t}-6v^{2}v_{x}+v_{xxx} = 0		 

v[t]- 6*(v)^(2)* v[x]+ v[x, x, x] = 0
 
Subscript[v, t]- 6*(v)^(2)* Subscript[v, x]+ Subscript[v, x, x, x] == 0
 Skipped - no semantic math Skipped - no semantic math - -
32.13#Ex1 z = x ⁒ ( 3 ⁒ t ) - 1 / 3 𝑧 π‘₯ superscript 3 𝑑 1 3 {\displaystyle{\displaystyle z=x(3t)^{-1/3}}}
z = x(3t)^{-1/3}		 

(x(+)*y*I) = (x(3*t))^(- 1/3)
 
(x[+]*y*I) == (x[3*t])^(- 1/3)
 Skipped - no semantic math Skipped - no semantic math - -
32.13#Ex2 v ⁒ ( x , t ) = ( 3 ⁒ t ) - 1 / 3 ⁒ w ⁒ ( z ) 𝑣 π‘₯ 𝑑 superscript 3 𝑑 1 3 𝑀 𝑧 {\displaystyle{\displaystyle v(x,t)=(3t)^{-1/3}w(z)}}
v(x,t) = (3t)^{-1/3}w(z)		 

v(x , t) = (3*t)^(- 1/3)* w*((x + y*I))
 
v[x , t] == (3*t)^(- 1/3)* w*((x + y*I))
 Skipped - no semantic math Skipped - no semantic math - -
32.13.E3 u t + 6 ⁒ u ⁒ u x + u x ⁒ x ⁒ x = 0 subscript 𝑒 𝑑 6 𝑒 subscript 𝑒 π‘₯ subscript 𝑒 π‘₯ π‘₯ π‘₯ 0 {\displaystyle{\displaystyle u_{t}+6uu_{x}+u_{xxx}=0}}
u_{t}+6uu_{x}+u_{xxx} = 0		 

u[t]+ 6*u*u[x]+ u[x, x, x] = 0
 
Subscript[u, t]+ 6*u*Subscript[u, x]+ Subscript[u, x, x, x] == 0
 Skipped - no semantic math Skipped - no semantic math - -
32.13#Ex3 z = x ⁒ ( 3 ⁒ t ) - 1 / 3 𝑧 π‘₯ superscript 3 𝑑 1 3 {\displaystyle{\displaystyle z=x(3t)^{-1/3}}}
z = x(3t)^{-1/3}		 

(x(+)*y*I) = (x(3*t))^(- 1/3)
 
(x[+]*y*I) == (x[3*t])^(- 1/3)
 Skipped - no semantic math Skipped - no semantic math - -
32.13#Ex5 z = x + 3 ⁒ Ξ» ⁒ t 2 𝑧 π‘₯ 3 πœ† superscript 𝑑 2 {\displaystyle{\displaystyle z=x+3\lambda t^{2}}}
z = x+3\lambda t^{2}		 

(x + y*I) = x + 3*lambda*(t)^(2)
 
(x + y*I) == x + 3*\[Lambda]*(t)^(2)
 Skipped - no semantic math Skipped - no semantic math - -
32.13#Ex6 u ⁒ ( x , t ) = W ⁒ ( z ) - Ξ» ⁒ t 𝑒 π‘₯ 𝑑 π‘Š 𝑧 πœ† 𝑑 {\displaystyle{\displaystyle u(x,t)=W(z)-\lambda t}}
u(x,t) = W(z)-\lambda t		 

u(x , t) = W*((x + y*I))- lambda*t
 
u[x , t] == W*((x + y*I))- \[Lambda]*t
 Skipped - no semantic math Skipped - no semantic math - -
32.13.E6 u x ⁒ t = sin ⁑ u subscript 𝑒 π‘₯ 𝑑 𝑒 {\displaystyle{\displaystyle u_{xt}=\sin u}}
u_{xt} = \sin@@{u}		 

u[x, t] = sin(u)

Subscript[u, x, t] == Sin[u]
Failure Failure
Failed [300 / 300]
Failed [300 / 300]
32.13#Ex7 z = x ⁒ t 𝑧 π‘₯ 𝑑 {\displaystyle{\displaystyle z=xt}}
z = xt		 

(x + y*I) = x*t
 
(x + y*I) == x*t
 Skipped - no semantic math Skipped - no semantic math - -
32.13#Ex8 u ⁒ ( x , t ) = v ⁒ ( z ) 𝑒 π‘₯ 𝑑 𝑣 𝑧 {\displaystyle{\displaystyle u(x,t)=v(z)}}
u(x,t) = v(z)		 

u(x , t) = v*((x + y*I))
 
u[x , t] == v*((x + y*I))
 Skipped - no semantic math Skipped - no semantic math - -
32.13.E8 u t ⁒ t = u x ⁒ x - 6 ⁒ ( u 2 ) x ⁒ x + u x ⁒ x ⁒ x ⁒ x subscript 𝑒 𝑑 𝑑 subscript 𝑒 π‘₯ π‘₯ 6 subscript superscript 𝑒 2 π‘₯ π‘₯ subscript 𝑒 π‘₯ π‘₯ π‘₯ π‘₯ {\displaystyle{\displaystyle u_{tt}=u_{xx}-6(u^{2})_{xx}+u_{xxxx}}}
u_{tt} = u_{xx}-6(u^{2})_{xx}+u_{xxxx}		 

u[t, t] = u[x, x]- 6*(u)^(2)[x, x]+ u[x, x, x, x]
 
Subscript[u, t, t] == Subscript[u, x, x]- 6*Subscript[(u)^(2), x, x]+ Subscript[u, x, x, x, x]
 Skipped - no semantic math Skipped - no semantic math - -
32.13#Ex9 z = x - c ⁒ t 𝑧 π‘₯ 𝑐 𝑑 {\displaystyle{\displaystyle z=x-ct}}
z = x-ct		 

(x + y*I) = x - c*t
 
(x + y*I) == x - c*t
 Skipped - no semantic math Skipped - no semantic math - -
32.13#Ex10 u ⁒ ( x , t ) = v ⁒ ( z ) 𝑒 π‘₯ 𝑑 𝑣 𝑧 {\displaystyle{\displaystyle u(x,t)=v(z)}}
u(x,t) = v(z)		 

u(x , t) = v*((x + y*I))
 
u[x , t] == v*((x + y*I))
 Skipped - no semantic math Skipped - no semantic math - -
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