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Question: Is it possible to obtain a simpler solution to this PDE in Maple?

Question:Is it possible to obtain a simpler solution to this PDE in Maple?

nm 8552 Maple 2019
pdsolve
May 20 2019
0

Maple is very good in solving PDE's. But this specific solution seems way too complicated when compared to Matematica solution, which I verified using Maple pdetest to be correct.

Is there a way to make Maple produce the simpler solution to this pde? simplify does nothing on the solution. May be by using a good HINT or such other option? 
 

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restart;
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pde:=(a*y+b*x+c)*diff(w(x,y),x)-(b*y+k*x+s)*diff(w(x,y),y)=0;

(a*y+b*x+c)*(diff(w(x, y), x))-(b*y+k*x+s)*(diff(w(x, y), y)) = 0

> 

sol:=pdsolve(pde,w(x,y))

w(x, y) = _F1(1/(a^3*k^2*y^2-2*a^2*b^2*k*y^2+2*a^2*b*k^2*x*y+a^2*k^3*x^2+a*b^4*y^2-4*a*b^3*k*x*y-2*a*b^2*k^2*x^2+2*b^5*x*y+b^4*k*x^2+2*a^2*c*k^2*y+2*a^2*k^2*s*x-4*a*b^2*c*k*y-4*a*b^2*k*s*x+2*b^4*c*y+2*b^4*s*x+a^2*k*s^2-a*b^2*s^2-2*a*b*c*k*s+a*c^2*k^2+2*b^3*c*s-b^2*c^2*k)^(1/2))

> 

mma_solution := w(x,y)= _F1( (2*s*x+k*x^2+2*c*y+2*b*x*y+a*y^2)/a );

w(x, y) = _F1((a*y^2+2*b*x*y+k*x^2+2*c*y+2*s*x)/a)

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pdetest(mma_solution,pde)

0

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Here is screen shot showing the other solution

Download q1.mw

 
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