For a PDE $(x-y^{2}) u_{x} + u_{y} = 0$ I've tried to use method of characteristics. But I've failed to do so. It was because of the term $x-y^{2}$; I don't know how to integrate this on the characteristic line. Should I try another method than method of chracteristic? Or is there a clever trick for this?
Related equatons: $dx/ds = x-y^{2}$, $dy/ds = 1$, $du/ds = 0$.