# Homework Help: 2nd Order D.E. help

1. May 7, 2006

### gbacsf

I'm have a lot of trouble trying to find the general solution to the following D.E.

y'' + 6.4y' + 10.24y = e^(-3.2x)

I get the homogeneous solution as

C1*e^(-3.2x)+C2*x*e^(-3.2x)

and the particular solution as 0

So a general solution of

Y=C1*e^(-3.2x)+C2*x*e^(-3.2x)

I know my solution is not right, there is some trick to it, any help?

Gab

Last edited: May 7, 2006
2. May 7, 2006

### arildno

You DO mean the diff.eq y''+6.4y'+10.24y=e^(-3.2x), right?

3. May 7, 2006

### gbacsf

Ops, yes I do.

4. May 7, 2006

### dav2008

The reason you obtained 0 as your particular solution in your approach is because the inhomogeneous term is also a solution to the homogeneous equation.

What should you do in that situation?

5. May 7, 2006

### gbacsf

uh? Variation of parameters to get something like

Yg=u1y1+u2y2+c1(x)y1+c2(x)y2

where Yh= u1y1+u2y2

and Yp=c1(x)y1+c2(x)y2

?

6. May 7, 2006

### gbacsf

So...

Yg= u1*e^(-3.2x)+u2*x*e^(-3.2x)+0.5*(X^2)*e^(-3.2x)

?