# Homework Help: Form of particular solution for y''-2y'+y=(e^2)/x

1. Apr 21, 2010

### filter54321

1. The problem statement, all variables and given/known data
Find the general solution for:
y''-2y'+y=ex/x

2. Relevant equations
NONE - not an initial value problem

3. The attempt at a solution
Solve the homogeneous first:
r2-2r+1=0
r=1 as a double root

So:

y1=c1ex
y2=c2xex

...but what in God's name is the form for the particular Y (based on the right side of the equation?). I suppose it's the "hard part" of this exercise but I've tried a couple and still don't see it.

Last edited: Apr 21, 2010
2. Apr 21, 2010

### LCKurtz

Do you type that right and really mean the right side is

$$\frac {e^2} x$$

If so, the method would be variation of parameters.

3. Apr 21, 2010

### filter54321

Right side corrected, should be y''-2y'+y=(ex)/x

4. Apr 21, 2010