Hello everyone. I have tried this problem a couple times and seem to get it wrong.
Find a particular solution to
Any help would be appreciated
its a bit tedeous...
firstly we have to consider the homogenous equation
which has solution
using the variation of parameters theorem we see that
with calculted using the Wronskian determinant
so we can then see that
and after substituting and turning the crank we end up with
which is simple to integrate, we then find the final answer of
The final anwer will then just be the superposition of the particular and complimentary solutions