Hi Folks,

Looking a sample exam question...

(i) Write down the general form of a semi linear first order PDE in u(x,y)

$\displaystyle a(x,y) \frac{\partial u}{\partial x} +b(x,y) \frac{\partial u}{\partial y}=h(x,y,u)$

(ii) Write down the ordinary differential equation satisfied by a characteristic curve in the xy plane for your pde in (i)

$\displaystyle \frac{dy}{dx}=\frac{b(x,y)}{a(x,y}$ and $\displaystyle a(x,y) \ne 0$

(iii)Give a careful consideration of the ordinary differential equation satisfied by u(x,y) along such a characteristic curve?

I have not found anything in my notes regarding this...May anyone help?

Thanks