# Thread: quasilinear pde

1. ## quasilinear pde

I have to solve the following quasilinear equation using the method of characteristics:

$x u_x + y u_y +yu=xy$
$u|_{y=x^2}=sin x$

$\frac{dx}{dt}=x$ gives me $ln x=t + c_1$
$\frac{dy}{dt}=y$ gives me $ln y=t+c_2$

But what do I do with $\frac{du}{dt}=xy - yu$?

Thank you.

2. Anyone? Please, it's really confusing and I need to understand it in order to go on..