# Math Help - pde, characteristic curves

1. ## pde, characteristic curves

Can someone help me with a headstart to this problem?

Find the no. of characteristic curves of the PDE

$(x^2 +2y) u_{xx}+ (y^3 - y +u ) u_{yy} + x^2 (y-1)u_{xy} + 3u_{x} + u = 0$

passing through the point x=1 and y=1.

2. ## Re: pde, characteristic curves

I found that this pde is parabolic.. Does it help us deduce that there are no characteristic curves passing through the given point?

I reckon that a parabolic pde has 1 characteristic curve, an elliptic has none and a hyperbolic has 2 characteristic curves... Am I right?