Can someone help me with a headstart to this problem?
Find the no. of characteristic curves of the PDE
$\displaystyle (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.
Can someone help me with a headstart to this problem?
Find the no. of characteristic curves of the PDE
$\displaystyle (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.
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?