# PDE help

1. Mar 8, 2010

### BustedBreaks

I'm following an algorithm my teacher gave us and I'm trying to understand it...

I'm trying to solve this PDE 2Ux-Uy+5U=10 with U(x,0)=0

First I need to solve the homogeneous equation.

So I set up the relation:
V(y)=U(2y+c, y)

to solve 2Ux-Uy=0

where the characteristic equation is y=1x/2 -c/2 and x=2y+c

***My first problem is that I am having a hard time understanding what the characteristic equation is and why it is important to use in solving this problem.

Then I need to to take the derivative of V(y) with respect to y

V ' (y) =(Ux)(Xy) + (Uy)(Yy) which is
V ' (y) =2Ux+Uy

here is my second problem, I seem to get 2Ux+Uy instead of 2Ux-2Uy which is what I need to make the problem a little easier...

EDIT... Finally got it, nvm...

Last edited: Mar 8, 2010