problem : Find the characteristic curves for pde $$ \frac{\partial^2 u}{\partial y^2} -y\frac{\partial^2 u}{\partial x^2}=0$$
if 1)$y<0$
2)$y>0$
3)$y=0$
4)$y \neq 0$
Solution:
1)Here characteristic curve is Ellipse
2) characteristic curve is hyperbola
3)characteristic curve is parabola
Am I doing right ?
