How do I solve the following second order partial differential equation?
$4u_{xx}+5u_{xy}+u_{yy}+u_x+u_y=2$
I have classified the equation to be hyperbolic and changed variables to obtain the canonical form as $u_{\epsilon\nu}={1\over{3u_\nu}}-{8\over9}$ which I believe is correct but I am struggling to find the general solution? A step by step solution would be appreciated.