
first order pde
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.