# Closed form solution to an ordinary differential equaiton

How to solve the following ordinary differential equation?

$$y'(x)= \frac{C_1}{y(x)} +C_2 C_3 \cos\left(C_3 x\right) +C_4$$

where $C_1, C_2, C_3, C_4\in \mathbb{R}$ are all constants.

It looks simple but difficult to solve.

• To me, it does not look simple at all ! – Claude Leibovici Feb 27 '16 at 10:40
• A much simpler similarly looking equation was found to have a rather nontrivial solution here. However it does not seem that in your case we can get to Riccati. So I tend to declare your equation unsolvable, at least for generic values of constants. – Start wearing purple Feb 27 '16 at 10:59
• I would suggest solve it numerically. – user103093 Feb 27 '16 at 15:13