u_{xx}-u_{y}+\gamma u=f(x,y)

**dwsmith** · January 17th 2011, 07:27 PM

Show that the equation

$u_{xx}-u_{y}+\gamma u=f(x,y)$ ,

where $\gamma$ is any constant, can be transformed into

$\omega_{xx}-\omega_y=\varphi(x,y)$

My book has yet to discuss inhomogeneous equations. How do I tackle this?

**Danny** · January 18th 2011, 04:16 AM

Try a substitution of the form

$u(x,y) = e^{ky}\omega(x,y)$

and see if tou can choose $k$ to eliminate the $\gamma u$ term.

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