# Homework Help: Differential Equations Method of Flexible guessing

1. Feb 16, 2012

### mike1967

1. The problem statement, all variables and given/known data
Find a particular solution Yp of the given equation. Primes denote deriviate with respect to x
(method of flexible guess)

2. Relevant equations
4y''+4y'+y=3xe^x

3. The attempt at a solution
when I used y=Ae^x as guess my A depended on x
So y=Axe^x gave me 12A+9Ax=3x
12A=0
9Ax=3x
does not work,
Before I go on to trying y=Ax^2e^x am I doing this right?

2. Feb 16, 2012

### Staff: Mentor

I don't know what you mean by "my A depended on x." A is a constant, so is not dependent on any variable.
Why don't you try yp = Aex + Bxex?

3. Feb 16, 2012

### mike1967

Yp=3/9xe^x-4/9e^x right?

4. Feb 16, 2012

### Dick

Right.

5. Feb 16, 2012

### Staff: Mentor

This is something you should get in the habit of checking for yourself. You've already done all the hard work. If 4yp'' + 4y' + yp $\equiv$ 3xex, then your solution is correct.