hi all(adsbygoogle = window.adsbygoogle || []).push({});

i have been trying to solve to following problem,

[tex]

\frac{\partial^2 u}{\partial x^2} - \frac{\partial^2 u}{\partial y^2}

+ 2\frac{\partial u}{\partial x} + u = 0

[/tex]

[tex]

u=u(x,y)

[/tex]

after a bit of work using the change of variables

[tex]

\zeta=\zeta(x,y)=y-x

[/tex]

and

[tex]

\eta=\eta(x,y)=y+x

[/tex]

i obtain

[tex]- 4\frac{\partial u}{\partial \zeta \partial \eta} = 2\frac{\partial u}{\partial\zeta} - 2\frac{\partial u}{\partial\eta}-u[/tex]

but i am unsure how to solve this, i used maple to solve this problem and it gave out a fairly harmless answer so i am pretty sure there would be any easy way to solve the above equation.

could someone kindly show me how to obtain a solution to this problem

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# Solving a partial DE

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