7.2.24 8.1

7.2.24.1 [753] problem number 1
7.2.24.2 [754] problem number 2
7.2.24.3 [755] problem number 3
7.2.24.4 [756] problem number 4
7.2.24.5 [757] problem number 5
7.2.24.6 [758] problem number 6
7.2.24.7 [759] problem number 7
7.2.24.8 [760] problem number 8
7.2.24.9 [761] problem number 9
7.2.24.10 [762] problem number 10
7.2.24.11 [763] problem number 11
7.2.24.12 [764] problem number 12
7.2.24.13 [765] problem number 13

7.2.24.1 [753] problem number 1

problem number 753

Added Feb. 4, 2019.

Problem 2.8.1.1 from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.

Solve for w(x,y) wx+(f(x)y+g(x))wy=0

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]];
 

{{w(x,y)c1(yexp(1xf(K[1])dK[1])1xexp(1K[2]f(K[1])dK[1])g(K[2])dK[2])}}

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'));
 

w(x,y)=_F1(ye(f(x)dx)(e(f(x)dx)g(x)dx))

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7.2.24.2 [754] problem number 2

problem number 754

Added Feb. 4, 2019.

Problem 2.8.1.2 from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.

Solve for w(x,y)

wx+(f(x)y+g(x)yk)wy=0

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]];
 

{{w(x,y)c1((k1)1xexp((k1)1K[2]f(K[1])dK[1])g(K[2])dK[2]+y1kexp((k1)1xf(K[1])dK[1]))}}

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'));
 

w(x,y)=_F1(yk+1e(k1)(f(x)dx)+(k1)(e(k1)(f(x)dx)g(x)dx))

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7.2.24.3 [755] problem number 3

problem number 755

Added Feb. 4, 2019.

Problem 2.8.1.3 from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.

Solve for w(x,y)

wx+(y2+f(x)ya2af(x))wy=0

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'));
 

w(x,y)=_F1((ay)(e2ax+f(x)dxdx)e2ax+f(x)dxay)

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7.2.24.4 [756] problem number 4

problem number 756

Added Feb. 4, 2019.

Problem 2.8.1.4 from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.

Solve for w(x,y)

wx+(y2+xf(x)y+f(x))wy=0

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]];
 

{{w(x,y)c1(exp(1xf(K[5])K[5]dK[5])x2y+x1xexp(1K[6]f(K[5])K[5]dK[5])K[6]2dK[6])}}

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'));
 

w(x,y)=_F1(xy(ex2f(x)2xdxdx)+xex2f(x)2xdx+ex2f(x)2xdxdxyx+1)

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7.2.24.5 [757] problem number 5

problem number 757

Added Feb. 4, 2019.

Problem 2.8.1.5 from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.

Solve for w(x,y)

wx((k+1)xky2xk+1f(x)y+f(x))wy=0

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'));
 

w(x,y)=_F1(xk+1exxk+1f(x)2k2xdx+(yxk+11)(k+1)(xkexk+1f(x)dxx2dx)yxk+11)

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7.2.24.6 [758] problem number 6

problem number 758

Added Feb. 4, 2019.

Problem 2.8.1.6 from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.

Solve for w(x,y)

wx+(f(x)y2+ayabb2f(x))wy=0

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'));
 

w(x,y)=_F1((by)(eax+2b(f(x)dx)f(x)dx)eax+2b(f(x)dx)by)

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7.2.24.7 [759] problem number 7

problem number 759

Added Feb. 4, 2019.

Problem 2.8.1.7 from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.

Solve for w(x,y)

wx+(f[x]y2axnf[x]y+anxn1)wy=0

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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7.2.24.8 [760] problem number 8

problem number 760

Added Feb. 4, 2019.

Problem 2.8.1.8 from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.

Solve for w(x,y)

wx+(f(x)y2+anxn1a2x2nf(x))wy=0

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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7.2.24.9 [761] problem number 9

problem number 761

Added Feb. 4, 2019.

Problem 2.8.1.9 from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.

Solve for w(x,y)

wx+(f(x)y2+g(x)ya2f(x)ag(x))wy=0

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'));
 

w(x,y)=_F1((ay)(e2a(f(x)dx)+g(x)dxf(x)dx)e2a(f(x)dx)+g(x)dxay)

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7.2.24.10 [762] problem number 10

problem number 762

Added Feb. 4, 2019.

Problem 2.8.1.10 from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.

Solve for w(x,y)

wx+(f(x)y2+g(x)y+anxn1axng(x)a2x2nf(x))wy=0

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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7.2.24.11 [763] problem number 11

problem number 763

Added Feb. 4, 2019.

Problem 2.8.1.11 from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.

Solve for w(x,y)

wx+(f(x)y2axng(x)y+anxn1+a2x2n(g(x)f(x)))wy=0

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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7.2.24.12 [764] problem number 12

problem number 764

Added Feb. 4, 2019.

Problem 2.8.1.12 from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.

Solve for w(x,y)

xwx+(f(x)y2+ny+ax2nf(x))wy=0

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]];
 

{{w(x,y)c1(tan1(yxna)a1xf(K[1])K[1]n1dK[1])}}

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'));
 

w(x,y)=_F1(a(xn1f(x)dx)arctan(yxna))

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7.2.24.13 [765] problem number 13

problem number 765

Added Feb. 4, 2019.

Problem 2.8.1.13 from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.

Solve for w(x,y)

xwx+(x2nf(x)y2+(axnf(x)n)y+bf(x))wy=0

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]];
 

{{w(x,y)c1(1xbf(K[5])K[5]2nbK[5]dK[5]2btan1(b(a2b2yx2nb)4ba2)4ba2)}}

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'));
 

w(x,y)=_F1(2(aarctanh((2yxn+a)a(a24b)a2)+(a24b)a2(xnf(x)xdx)2)a(a24b)a2)

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