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.

  • 3
    $\begingroup$ To me, it does not look simple at all ! $\endgroup$ – Claude Leibovici Feb 27 '16 at 10:40
  • 4
    $\begingroup$ 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. $\endgroup$ – Start wearing purple Feb 27 '16 at 10:59
  • $\begingroup$ I would suggest solve it numerically. $\endgroup$ – user103093 Feb 27 '16 at 15:13

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