I'm having trouble trying to solve the differential equation $\displaystyle y^{(2)} + (\frac{1}{4t^2})y=f cos(t), t>0$ given that $\displaystyle y_{1}=\sqrt{t}$ is a solution of the homogeneous equation. I have been trying to solve this by reduction of order and am having no luck. I beleive the correct answer to be $\displaystyle y(t)=\sqrt{t}[c_{1}+c_{2}ln(t)+\int_0^t f \sqrt{s} cos(s)[ln(t)-ln(s)]ds]$ but can't seem to figure it out. Any help would be appreciated.