(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

U_{tt}-U_{xx}+2U_{xy}-U_{yy}=0

with the conditions:

U(1,x,y)=cos(x)+e^{y}

U_{t}(1,x,y)=sin(x)-y^{2}

2. Relevant equations

Not using separation of variables to solve.

3. The attempt at a solution

I've gotten the general equation to be of the form:

U(t,x,y)=ψ(x+t,y-t)+ζ(x-t,y+t)

but solving for the initial conditions is giving me a problem:

ψ(x+1,y-1)= sin(x)+e^{y}-ζ(x-1,y+1)

ψ_{1}(x+1,y-1)=-cos(x)-ζ_{1}(x-1,y+1)

ψ_{2}(x+1,y-1)=-e^{y}-ζ_{2}(x-1,y+1)

subbing that into the U_{t}and simplifying gives me this:

2 ζ_{1}+2 sin(X) = 2ζ_{2}-e^{y}+y^{2}

which I'm not sure what to do with...

help greatly apreciated

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# Partial Differential Equations

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