Non-homogeneous Partial Differential Equation with trigonometric coefficient

Question

Is there a general method to determine an analytic particular solution of the equation $$ -2(12+x)\frac{\partial f}{\partial y}+4\frac{\partial^2f}{\partial x\partial y}=\cos x? $$

Answer 1

$$-2(12+x)\frac{\partial f}{\partial y}+4\frac{\partial^2f}{\partial x\partial y}=\cos x$$ Rewrite it as a first order differential equation $$-2(12+x)p+4\frac {dp}{dx}=\cos x$$ $$(12+x)p-2p'=-\frac {\cos x}2$$

Where $p=\frac {\partial f}{\partial y}$

Not sure it can be integrated with elementary functions