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 :
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.