Laplace DE separation of variables

[accountkiller]

Homework Statement

I'm supposed to find a nontrivial solution to tx'' + (t-2)x' + x = 0, x(0) = 0. You don't really need to know that but just in case.

I got to this point:
(s+1)X'(s) + 4X(s) = 0

Now I need to separate variables to find a solution but I've been working on this for two days and can't figure out how to get to the correct solution, which is:
X(s) = C/(s+1)^4

So my question is, how do I go from the first equation to the second using separation of variables?

Homework Equations

The Attempt at a Solution

I've been trying for two days now.. with X(s) = X and X'(s) = dX/ds, I separated all X's and dX's and the same with s and ds.. then when I took the integral of both sides, I get natural logs since I'm doing the integral of 1/x and 1/(s+1) ... I don't know where to go with natural logs, since that's not the answer.

Any help would be appreciated, thanks!

 

[lanedance]

as you have natural log on both sides, you should be able to remove it by raising both sides to the power of e...

 

[accountkiller]

Ah, right! That solves my entire dilemma! *phew* thanks so much for pointing that out ;)

 

[lanedance]

scratch that