# Thread: first order PDE

1. ## first order PDE

1. Solve the equation:

$\displaystyle x_{2}\frac{\partial u}{\partial x_{1}}-x_{1}\frac{\partial u}{\partial x_{2}}=f$

What can be a noncharacteristic initial curve?

2. Solve:

$\displaystyle u\frac{\partial u}{\partial x_{1}}+\frac{\partial u}{\partial x_{2}}=1$
$\displaystyle u=\frac{s}{2} , x_{1}=x_{2}=s, 0<s<1$

2. "Solve", no. Help, yes. What have you done on this yourself?