Added Feb. 9, 2019.
Problem Chapter 3.2.2.1 from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.
Solve for
Mathematica ✓
ClearAll["Global`*"]; pde = a*D[w[x, y], x] + b*D[w[x, y], y] == c*x^2 + d*y^2 + k*x*y + n; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]];
Maple ✓
restart; pde := a* diff(w(x,y),x)+b*diff(w(x,y),y) = c*x^2+d*y^2+k*x*y+n; cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,w(x,y)) ),output='realtime'));
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Added Feb. 9, 2019.
Problem Chapter 3.2.2.2 from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.
Solve for
Mathematica ✓
ClearAll["Global`*"]; pde = a*x*D[w[x, y], x] + b*y*D[w[x, y], y] == c*x^2 + d*y^2 + k*x*y + n; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]];
Maple ✓
restart; pde := a*x*diff(w(x,y),x)+b*y*diff(w(x,y),y) = c*x^2+d*y^2+k*x*y+n; cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,w(x,y)) ),output='realtime'));
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Added Feb. 9, 2019.
Problem Chapter 3.2.2.3 from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.
Solve for
Mathematica ✓
ClearAll["Global`*"]; pde = a*y*D[w[x, y], x] + b*x*D[w[x, y], y] == c*x*y + d; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]];
Maple ✓
restart; pde := a*y*diff(w(x,y),x)+b*x*diff(w(x,y),y) = c*x*y+d; cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,w(x,y)) ),output='realtime'));
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Added Feb. 9, 2019.
Problem Chapter 3.2.2.4 from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.
Solve for
Mathematica ✓
ClearAll["Global`*"]; pde = a*x^2*D[w[x, y], x] + b*y^2*D[w[x, y], y] == c*x^2 + d*y^2 + k*x*y + n*x + m*y + s; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]];
Maple ✓
restart; pde := a*x^2*diff(w(x,y),x)+b*y^2*diff(w(x,y),y) =c*x^2+d*y^2+ k*x*y+ n*x+ m*y+s; cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,w(x,y)) ),output='realtime'));
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Added Feb. 9, 2019.
Problem Chapter 3.2.2.5 from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.
Solve for
Mathematica ✓
ClearAll["Global`*"]; pde = x^2*D[w[x, y], x] + a*x*y*D[w[x, y], y] == b*y^2; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]];
Maple ✓
restart; pde := x^2*diff(w(x,y),x)+a*x*y*diff(w(x,y),y) =b*y^2; cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,w(x,y)) ),output='realtime'));
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Added Feb. 9, 2019.
Problem Chapter 3.2.2.6 from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.
Solve for
Mathematica ✓
ClearAll["Global`*"]; pde = a*y^2*D[w[x, y], x] + b*x^2*D[w[x, y], y] == c*x^2 + d; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]];
Maple ✓
restart; pde := a*y^2*diff(w(x,y),x)+b*x^2*diff(w(x,y),y) =c*x^2+d; cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,w(x,y)) ),output='realtime'));
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Added Feb. 9, 2019.
Problem Chapter 3.2.2.7 from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.
Solve for
Mathematica ✓
ClearAll["Global`*"]; pde = a*y^2*D[w[x, y], x] + b*x*y*D[w[x, y], y] == c*x^2 + d*y^2; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]];
Maple ✓
restart; pde := a*y^2*diff(w(x,y),x)+b*x*y*diff(w(x,y),y) =c*x^2+d*y^2; cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,w(x,y)) ),output='realtime'));
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