Hi, I am having difficulty doing these 2 questions. I tried the change of coordinates but that got very messy and got me nowhere.

Reduce to canonical form:

1. $\displaystyle y^2u_{xx}+2xyu_{xy}+x^2u_{yy}=0$

2. $\displaystyle u_{xx}-2xyu_{xy}=0$, $\displaystyle (x \ne 0)$

Thanks for your help.