- #1
accountkiller
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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!