Hi all,

I'm currently doing a problem based on reduction of order. The question goes:

Consider the DE

. Given that

, find a second linearly independent solution.

I can see that the solution to this equation is in the form

. That means

. After rearrange the DE to

, I can see that the LDE for

will be of the form

. This simplified to the LDE

.

To solve for

, I found an integrating factor

. Using this integrating factor, solving for

:

Therefore

When integrating to find u, I'm left with this horrible equation:

I feel this is completely wrong.

I was wondering if someone could look over my work here and point me in the right direction.

Thank you in advance.