Folks,

I believe this 2nd order PDE is elliptic. I want to make sure new coordinates are correct before I find the canonical form.

$\displaystyle \displaystyle u_{xx}+2u_{yx}+5u_{yy}-2u_x+u=0 \implies \frac{dy}{dx}=1 \pm \sqrt{-4}=1 \pm 2i \therefore$

$\displaystyle \displaystyle y=\int 1 \pm 2i dx= x \pm i 2x +constant$

The constants are in the form $\displaystyle \phi(x,y)-i \psi(x,y)=constant$

I choose for my new co ordinates $\displaystyle s(x,y)=y-x$ and$\displaystyle t(x,y)=-2x$

Are s and t correct?

thanks