Can someone please help to solve the following SDE: $$ dX_t=\cos(t)\,dW_t-\tan(t)X_t\,dt, ~~ X_0=0? $$ My idea is to start in this way: $$ X_t = 0 + \int \cos(t)\,dW_t - \int \tan(t)X_t\,dt , $$ but here I have the problem with $X_t$ on the right side.
Is my beginning of solving even correct? Should I start in different way?
thank you in advance
You get a directly solvable equation if you apply the Ito transformation theorem (chain rule for SDE) to $$ Y_t=F(t,X_t)=\frac{X_t}{\cos(t)}. $$