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The Attempt at a Solution
I don't have any background in linear algebra, so I can't use cramers rule as a heads up, so I have to solve the system of equations (no linear algebra for this course is needed).
Ok, so I take the auxiliary, r^2=-25, r=+/-5i
u_1'cos(5x)+u_2'sin(5x) = 0
-5u_1'sin(5x)+5u_2'cos(5x) = cot(5x)
I am stumped at how to solve this system of equations. I think the rest before it is right..?
Seems like the algebra has got me.