Question: Use the variation of parameter method to find the general solution of the following differential equation $$(\cos x) y''+(2\sin x) y'-(\cos x) y =0\;\;\;\;,\;\;\;\;0<x<1$$
I think the question is wrong, since the right hand side term is 0, so the particular integral will also be zero. Thus, the general solution will be equal to homogenous solution. So, I think no use of using the variation of parameter formulas since $y_p(x)=0$ always. I reduced the equation as in the subject or title and then used integrating factor $$y=(\cos x )z$$ to eliminate the term $y'$ but I got another difficult DE as $z''-2\sec^2xz=0$
Please help with any suggestions or do you think question is correct. Is there a way to solve it ?