- #1
jimmycricket
- 116
- 2
Homework Statement
suppose [tex]u(x,y)[/tex] satisfies the partial differential equation:
[tex]-4y\frac{\partial u}{\partial x}+\frac{\partial u}{\partial y}=0[/tex]
Find the characteristic curves for this equation and name the shape they form
The Attempt at a Solution
[tex]\frac{dy}{dt}=1 \Longrightarrow y=t+y_0[/tex]
[tex]\frac{dx}{dt}=-4y=-4(t+y_0) \Longrightarrow x=-2t^2-4y_0t+x_0[/tex]
What can I say about the shape these curves form?