Well I have given the following PDE:
$y\cdot\partial_xu(x,y)+\partial_yu(x,y)=0$
Now I have to solve it by using the method of characteristics.
The coefficient are $(a,b,c)=(y,1,0)$. Then I have to solve the following differential equations: $\dot x(t) = y$ and $\dot y=1$. $\Longrightarrow y(t)=t+c$ and $x(t)=\frac {t^2}2+tc +d$ with any constant numbers $c,d$.
But now I don't know how to continue. How do I get $u(x,y)$ and is my ansatz correct?
Thanks for helping!!