Let $u=u(x,y)$. Now make the change of variables $x=x(r,θ)=r\cos θ$, $y=y(r,θ)=r\sin θ$. Express the Laplacian of $u$: $∂^2 u/∂x^2 + ∂^2 u/∂y^2$ in terms of derivatives of $u$ with respect to $r$ and $θ$ and everything should be in terms of $r$ and $θ$ with also the assumption that all partials are continuous.
Express the Laplacian of $u \ldots ∂$
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ordinary-differential-equations