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  • 4 years ago

PDEs, help with initial value Problem: \[u_{tt}−u_{xx}+2u_{xy}−u_{yy}=0 \text{ with conditions }u(1,x,y)=\cos (x)+e^y\] \[\text{and} u_t(1,x,y)=\sin (x)−y^2\] I've gotten the solution to the point where I've solved for the general case and gotten: \[u=ψ(x+t,y−t)+ϕ(x−t,y+t)\] where phi and psi are arbitrary functions, but attempting to solve the initial conditions has resulted in nothing but problems, any help at all would be great.

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