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Question: Solve system for unknown function

Question:Solve system for unknown function

Zeineb 520 Maple
solve
April 30 2019
0

I

have the following function phi(x,y) which depends on two unknown functions F1 and F2 which are differentiable.

Phi(x,y)=y sin(x y) + F1(y) + y^2 F2(x y)

Note that F1 and F2 are obtained by hand when I solve a partial differential equation

I would like to find  phi(x,y)  that satisfies phi=1 and diff(phi(x,y),y)=1-x^2*cos(x^2) on line y=x

 

constraint.mw

Thanks for your help

 
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