Added December 1, 2019.
Problem Chapter 8.8.1.1, from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.
Solve for
Mathematica ✓
ClearAll["Global`*"]; pde = D[w[x,y,z],x]+f[x]*D[w[x,y,z],y]+g[x]*D[w[x,y,z],z]==(h2[x]*y+h1[x]*z+h0[x])*w[x,y,z]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x,y,z}], 60*10]];
Maple ✓
restart; local gamma; pde := diff(w(x,y,z),x)+ f(x)*diff(w(x,y,z),y)+ g(x)*diff(w(x,y,z),z)= (h2(x)*y+h1(x)*z+h0(x))*w(x,y,z); cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,w(x,y,z))),output='realtime'));
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Added December 1, 2019.
Problem Chapter 8.8.1.2, from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.
Solve for
Mathematica ✓
ClearAll["Global`*"]; pde = D[w[x,y,z],x]+f[x]*(y+a)*D[w[x,y,z],y]+g[x]*(z+b)*D[w[x,y,z],z]==h[x]*w[x,y,z]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x,y,z}], 60*10]];
Maple ✓
restart; local gamma; pde := diff(w(x,y,z),x)+ f(x)*(y+a)*diff(w(x,y,z),y)+ g(x)*(z+b)*diff(w(x,y,z),z)= h(x)*w(x,y,z); cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,w(x,y,z))),output='realtime'));
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Added December 1, 2019.
Problem Chapter 8.8.1.3, from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.
Solve for
Mathematica ✓
ClearAll["Global`*"]; pde = D[w[x,y,z],x]+(a*y+f[x])*D[w[x,y,z],y]+(b*z+g[x])*D[w[x,y,z],z]==h[x]*w[x,y,z]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x,y,z}], 60*10]];
Maple ✓
restart; local gamma; pde := diff(w(x,y,z),x)+ (a*y+f(x))*diff(w(x,y,z),y)+ (b*z+g(x))*diff(w(x,y,z),z)= h(x)*w(x,y,z); cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,w(x,y,z))),output='realtime'));
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Added December 1, 2019.
Problem Chapter 8.8.1.4, from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.
Solve for
Mathematica ✓
ClearAll["Global`*"]; pde = D[w[x,y,z],x]+(f1[x]*y+f2[x])*D[w[x,y,z],y]+(g1[x]*y+g2[x])*D[w[x,y,z],z]==(h2[x]*y+h1[x]*z+h0[x])*w[x,y,z]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x,y,z}], 60*10]];
Maple ✓
restart; local gamma; pde := diff(w(x,y,z),x)+ (f1(x)*y+f2(x))*diff(w(x,y,z),y)+ (g1(x)*y+g2(x))*diff(w(x,y,z),z)= (h2(x)*y+h1(x)*z+h0(x))*w(x,y,z); cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,w(x,y,z))),output='realtime'));
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Added December 1, 2019.
Problem Chapter 8.8.1.5, from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.
Solve for
Mathematica ✓
ClearAll["Global`*"]; pde = D[w[x,y,z],x]+(f1[x]*y+f2[x])*D[w[x,y,z],y]+(g1[x]*z+g2[x])*D[w[x,y,z],z]==(h2[x]*y+h1[x]*z+h0[x])*w[x,y,z]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x,y,z}], 60*10]];
Maple ✓
restart; local gamma; pde := diff(w(x,y,z),x)+ (f1(x)*y+f2(x))*diff(w(x,y,z),y)+ (g1(x)*z+g2(x))*diff(w(x,y,z),z)= (h2(x)*y+h1(x)*z+h0(x))*w(x,y,z); cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,w(x,y,z))),output='realtime'));
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Added December 1, 2019.
Problem Chapter 8.8.1.6, from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.
Solve for
Mathematica ✓
ClearAll["Global`*"]; pde = D[w[x,y,z],x]+(y^2-a^2+a*lambda*Sinh[lambda*x]-a^2*Sinh[lambda*x]^2)*D[w[x,y,z],y]+f[x]*Sinh[gamma*z]*D[w[x,y,z],z]==g[x]*w[x,y,z]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x,y,z}], 60*10]];
Maple ✓
restart; local gamma; pde := diff(w(x,y,z),x)+ (y^2-a^2+a*lambda*sinh(lambda*x)-a^2*sinh(lambda*x)^2)*diff(w(x,y,z),y)+ f(x)*sinh(gamma*z)*diff(w(x,y,z),z)= g(x)*w(x,y,z); cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,w(x,y,z))),output='realtime'));
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Added December 1, 2019.
Problem Chapter 8.8.1.7, from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.
Solve for
Mathematica ✓
ClearAll["Global`*"]; pde = D[w[x,y,z],x]+( f1[x]*y+f2[x]*y^k)*D[w[x,y,z],y]+(g1[x]*z+g2[x]*z^m)*D[w[x,y,z],z]==h[x]*w[x,y,z]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x,y,z}], 60*10]];
Maple ✓
restart; local gamma; pde := diff(w(x,y,z),x)+ ( f1(x)*y+f2(x)*y^k)*diff(w(x,y,z),y)+ (g1(x)*z+g2(x)*z^m)*diff(w(x,y,z),z)= h(x)*w(x,y,z); cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,w(x,y,z))),output='realtime'));
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Added December 1, 2019.
Problem Chapter 8.8.1.8, from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.
Solve for
Mathematica ✗
ClearAll["Global`*"]; pde = D[w[x,y,z],x]+( f1[x]*y+f2[x]*y^k)*D[w[x,y,z],y]+(g1[x]+g2[x]*Exp[lambda*z])*D[w[x,y,z],z]==h[x]*w[x,y,z]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x,y,z}], 60*10]];
Failed
Maple ✓
restart; local gamma; pde := diff(w(x,y,z),x)+ ( f1(x)*y+f2(x)*y^k)*diff(w(x,y,z),y)+ (g1(x)+g2(x)*exp(lambda*z))*diff(w(x,y,z),z)= h(x)*w(x,y,z); cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,w(x,y,z))),output='realtime'));
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Added December 1, 2019.
Problem Chapter 8.8.1.9, from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.
Solve for
Mathematica ✗
ClearAll["Global`*"]; pde = D[w[x,y,z],x]+( f1[x]+f2[x]*Exp[lambda*y])*D[w[x,y,z],y]+(g1[x]+g2[x]*Exp[beta*z])*D[w[x,y,z],z]==h[x]*w[x,y,z]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y,z], {x,y,z}], 60*10]];
Failed
Maple ✓
restart; local gamma; pde := diff(w(x,y,z),x)+ ( f1(x)+f2(x)*exp(lambda*y))*diff(w(x,y,z),y)+ (g1(x)+g2(x)*exp(beta*z))*diff(w(x,y,z),z)= h(x)*w(x,y,z); cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,w(x,y,z))),output='realtime'));
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