# Is this diff eq solvable?

1. Feb 29, 2008

Is this diff eq solvable? !!!

1. The problem statement, all variables and given/known data
Find the general solution to the third order homogeneous diff eq if one solution is known to be:

$$x^2e^{5x}$$

I was thinking of using reduction of order but I don't have the original equation!

2. Feb 29, 2008

Okay. Since it was given that the 3rd order diff eq is homogeneous, it is okay to assume that there is no particular solution to this, right?

And I can also assume that (m-5) is a factor of the characteristic equation. I am also assuming that it is a thrice repeated root, so $y=c_1e^{5x}+c_2xe^{5x}+c_3x^2e^{5x}$

I am not so confident in this, since it is all based on assumption. Any thoughts on the validity of this?

3. Feb 29, 2008

### d_leet

It might help a bit if you told us what the differential equation was.

4. Feb 29, 2008

Read the OP. It has not been given.

5. Feb 29, 2008

### HallsofIvy

Staff Emeritus
Assuming this is a linear homogeneous 3rd order diff eq with constant coefficients, then that is the case and the differential equation must be (D- 5)3y= y"'-15y"+ 75y'- 125y= 0. Of course, we were not told that.

Last edited: Feb 29, 2008
6. Feb 29, 2008