How can we solve (if a closed form expression for f(x) can be found) the following first-order linear differential equation?
$$f'(x)=f(x)\cdot (\cos x+\tan x)$$
I have found that one function which validates this equation is: $$f(x)=\frac{e^{\sin x}}{\cos x}$$
HINT Separation of variables yields $$ \int \frac{f'(x)dx}{f(x)} = \int (\cos x + \tan x) dx $$ and LHS integrates to $\ln f(x) + C$.