I have a task where I have to write following differential equation as $y' = f(x)g(y)$ but I see no way you could factor it into two functions each only depending on $x$ respectively $y$:
$$y' = \exp\left[-x \cos(x) + \sin(x)+ 4x\right] + x\sin(x)y$$
Do you know a way of factoring this or can you confirm that you cannot factor this?
Hint(This may be considered cheating); You can solve for $y(x)$ with the D.E given, differentiate the solution, name the result of differentiation $f(x)$ and let $g(y)=1$.