Hi, need some help here so thanks to any replies.

PDE: $\displaystyle yu_x+2xyu_y=y^2$

a) characteristic equations:

$\displaystyle dx/ds=y$, $\displaystyle dy/ds=2xy$, $\displaystyle du/ds=y^2$

b) find dy/dx and solve

$\displaystyle dy/dx=dy/ds * ds/dx = x/y$

$\displaystyle ydy=xdx$

$\displaystyle y^2/2=x^2/2 +c$

$\displaystyle y=\pm \sqrt{x^2+2c}$

c) general solution

d) solve PDE

e) find u(x,y)

here I should be finding du/ds and solve after letting x(s)=? and y(s)=?

I need some help, so thanks guys.