63 HFOPDE, chapter 2.8.3

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63.1 problem number 1

problem number 584

Added Feb. 7, 2019.

Problem 2.8.3.1 from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.

Solve for \(w(x,y)\)

\[ w_x + \left (f(x) y^2 - a^2 f(x) + a \lambda \sinh (\lambda x) - a^2 f(x) \sinh ^2(\lambda x) \right ) w_y = 0 \]

Mathematica ✗

ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f]; 
 pde = D[w[x, y], x] + (f[x]*y^2 - a^2*f[x] + a*lambda*Sinh[lambda*x] - a^2*f[x]*Sinh[lambda*x]^2)*D[w[x, y], y] == 0; 
 sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]];
 

\[ \text {Failed} \]

Maple ✗

 
w:='w';x:='x';y:='y';a:='a';b:='b';n:='n';m:='m';c:='c';k:='k';alpha:='alpha';beta:='beta';g:='g';A:='A';f:='f'; 
C:='C';lambda:='lambda';B:='B';mu:='mu';d:='d';s:='s';v:='v'; 
pde := diff(w(x,y),x)+(   f(x)*y^2 - a^2*f(x) + a*lambda*sinh(lambda*x) - a^2*f(x)*sinh(lambda*x)^2)*diff(w(x,y),y) = 0; 
cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,w(x,y)) ),output='realtime'));
 

\[ \text { sol=() } \]

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63.2 problem number 2

problem number 585

Added Feb. 7, 2019.

Problem 2.8.3.2 from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.

Solve for \(w(x,y)\)

\[ w_x + \left (f(x) y^2 - a(a f(x)+\lambda ) \tanh ^2(\lambda x) +a \lambda \right ) w_y = 0 \]

Mathematica ✗

ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f]; 
 pde = D[w[x, y], x] + (f[x]*y^2 - a*(a*f[x] + lambda)*Tanh[lambda*x]^2 + a*lambda)*D[w[x, y], y] == 0; 
 sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]];
 

\[ \text {Failed} \]

Maple ✗

 
w:='w';x:='x';y:='y';a:='a';b:='b';n:='n';m:='m';c:='c';k:='k';alpha:='alpha';beta:='beta';g:='g';A:='A';f:='f'; 
C:='C';lambda:='lambda';B:='B';mu:='mu';d:='d';s:='s';v:='v'; 
pde := diff(w(x,y),x)+(   f(x)*y^2 - a*(a*f(x)+lambda)*tanh(lambda*x)^2 +a*lambda)*diff(w(x,y),y) = 0; 
cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,w(x,y)) ),output='realtime'));
 

\[ \text { sol=() } \]

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63.3 problem number 3

problem number 586

Added Feb. 7, 2019.

Problem 2.8.3.3 from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.

Solve for \(w(x,y)\)

\[ w_x + \left (f(x) y^2 - a(a f(x)+\lambda ) \coth ^2(\lambda x) +a \lambda \right ) w_y = 0 \]

Mathematica ✗

ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s, lambda, B, s, mu, d, g, B, v, f]; 
 pde = D[w[x, y], x] + (f[x]*y^2 - a*(a*f[x] + lambda)*Coth[lambda*x]^2 + a*lambda)*D[w[x, y], y] == 0; 
 sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]];
 

\[ \text {Failed} \]

Maple ✗

 
w:='w';x:='x';y:='y';a:='a';b:='b';n:='n';m:='m';c:='c';k:='k';alpha:='alpha';beta:='beta';g:='g';A:='A';f:='f'; 
C:='C';lambda:='lambda';B:='B';mu:='mu';d:='d';s:='s';v:='v'; 
pde := diff(w(x,y),x)+(   f(x)*y^2 - a*(a*f(x)+lambda)*coth(lambda*x)^2 +a*lambda)*diff(w(x,y),y) = 0; 
cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,w(x,y)) ),output='realtime'));
 

\[ \text { sol=() } \]