Added Feb. 4, 2019.
Problem 2.8.1.1 from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.
Solve for
Mathematica ✓
ClearAll["Global`*"]; pde = D[w[x, y], x] + (f[x]*y + g[x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]];
Maple ✓
restart; pde := diff(w(x,y),x)+( f(x)*y+g(x) )*diff(w(x,y),y) = 0; cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,w(x,y))),output='realtime'));
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Added Feb. 4, 2019.
Problem 2.8.1.2 from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.
Solve for
Mathematica ✓
ClearAll["Global`*"]; pde = D[w[x, y], x] + (f[x]*y + g[x]*y^k)*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]];
Maple ✓
restart; pde := diff(w(x,y),x)+( f(x)*y+g(x)*y^k )*diff(w(x,y),y) = 0; cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,w(x,y))),output='realtime'));
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Added Feb. 4, 2019.
Problem 2.8.1.3 from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.
Solve for
Mathematica ✗
ClearAll["Global`*"]; pde = D[w[x, y], x] + (y^2 + f[x]*y - a^2 - a*f[x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]];
Failed
Maple ✓
restart; pde := diff(w(x,y),x)+( y^2+f(x)*y -a^2 -a*f(x) )*diff(w(x,y),y) = 0; cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,w(x,y))),output='realtime'));
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Added Feb. 4, 2019.
Problem 2.8.1.4 from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.
Solve for
Mathematica ✓
ClearAll["Global`*"]; pde = D[w[x, y], x] + (y^2 + x*f[x]*y + f[x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]];
Maple ✓
restart; pde := diff(w(x,y),x)+( y^2+x*f(x)*y + f(x))*diff(w(x,y),y) = 0; cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,w(x,y))),output='realtime'));
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Added Feb. 4, 2019.
Problem 2.8.1.5 from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.
Solve for
Mathematica ✗
ClearAll["Global`*"]; pde = D[w[x, y], x] - ((k + 1)*x^k*y^2 - x^(k + 1)*f[x]*y + f[x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]];
Failed
Maple ✓
restart; pde := diff(w(x,y),x)-( (k+1)*x^k*y^2-x^(k+1)*f(x)*y+f(x))*diff(w(x,y),y) = 0; cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,w(x,y))),output='realtime'));
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Added Feb. 4, 2019.
Problem 2.8.1.6 from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.
Solve for
Mathematica ✗
ClearAll["Global`*"]; pde = D[w[x, y], x] + (f[x]*y^2 + a*y - a*b - b^2*f[x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]];
Failed
Maple ✓
restart; pde := diff(w(x,y),x)+( f(x)*y^2+a*y-a*b- b^2*f(x))*diff(w(x,y),y) = 0; cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,w(x,y))),output='realtime'));
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Added Feb. 4, 2019.
Problem 2.8.1.7 from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.
Solve for
Mathematica ✗
ClearAll["Global`*"]; pde = D[w[x, y], x] + (f[x]*y^2 - a*x^n*f[x]*y + a*n*x^(n - 1))*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]];
Failed
Maple ✗
restart; pde := diff(w(x,y),x)+( f(x)*y^2-a*x^n*f(x)*y+a*n*x^(n-1))*diff(w(x,y),y) = 0; cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,w(x,y))),output='realtime'));
sol=()
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Added Feb. 4, 2019.
Problem 2.8.1.8 from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.
Solve for
Mathematica ✗
ClearAll["Global`*"]; pde = D[w[x, y], x] + (f[x]*y^2 + a*n*x^(n - 1) - a^2*x^(2*n)*f[x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]];
Failed
Maple ✗
restart; pde := diff(w(x,y),x)+( f(x)*y^2+a*n*x^(n-1)-a^2*x^(2*n)*f(x))*diff(w(x,y),y) = 0; cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,w(x,y))),output='realtime'));
sol=()
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Added Feb. 4, 2019.
Problem 2.8.1.9 from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.
Solve for
Mathematica ✗
ClearAll["Global`*"]; pde = D[w[x, y], x] + (f[x]*y^2 + g[x]*y - a^2*f[x] - a*g[x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]];
Failed
Maple ✓
restart; pde := diff(w(x,y),x)+( f(x)*y^2+g(x)* y-a^2*f(x)-a*g(x))*diff(w(x,y),y) = 0; cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,w(x,y))),output='realtime'));
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Added Feb. 4, 2019.
Problem 2.8.1.10 from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.
Solve for
Mathematica ✗
ClearAll["Global`*"]; pde = D[w[x, y], x] + (f[x]*y^2 + g[x]*y + a*n*x^(n - 1) - a*x^n*g[x] - a^2*x^(2*n)*f[x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]];
Failed
Maple ✗
restart; pde := diff(w(x,y),x)+( f(x)*y^2+g(x)*y+a*n*x^(n-1) - a*x^n*g(x)-a^2*x^(2*n)*f(x))*diff(w(x,y),y) = 0; cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,w(x,y))),output='realtime'));
sol=()
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Added Feb. 4, 2019.
Problem 2.8.1.11 from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.
Solve for
Mathematica ✗
ClearAll["Global`*"]; pde = D[w[x, y], x] + (f[x]*y^2 - a*x^n*g*x*y + a*n*x^(n - 1) + a^2*x^(2*n)*(g*x - f*x))*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]];
Failed
Maple ✗
restart; pde := diff(w(x,y),x)+( f(x)*y^2-a*x^n*g(x)*y+a*n*x^(n-1)+a^2*x^(2*n)*(g(x)-f(x)))*diff(w(x,y),y) = 0; cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,w(x,y))),output='realtime'));
sol=()
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Added Feb. 4, 2019.
Problem 2.8.1.12 from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.
Solve for
Mathematica ✓
ClearAll["Global`*"]; pde = x*D[w[x, y], x] + (f[x]*y^2 + n*y + a*x^(2*n)*f[x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}, Assumptions -> a > 0], 60*10]];
Maple ✓
restart; pde := x*diff(w(x,y),x)+( f(x)*y^2+n*y+a*x^(2*n)*f(x))*diff(w(x,y),y) = 0; cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,w(x,y)) assuming a>0),output='realtime'));
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Added Feb. 4, 2019.
Problem 2.8.1.13 from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.
Solve for
Mathematica ✓
ClearAll["Global`*"]; pde = x*D[w[x, y], x] + (x^(2*n)*f[x]*y^2 + (a*x^n*f[x] - n)*y + b*f[x])*D[w[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]];
Maple ✓
restart; pde := x* diff(w(x,y),x)+( x^(2*n)* f(x)*y^2+(a*x^n*f(x)-n)*y+b*f(x))*diff(w(x,y),y) = 0; cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,w(x,y)) ),output='realtime'));
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