Question: Solve system for unknown function


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

Thanks for your help


Please Wait...