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I have tried to find hints using Mathematica but it did not worked. I can not able to convert problem into any form Which I know how to solve this DE. Can you give me a hint? $$(1+e^y)\cos (t)dt + e^y\sin (y)dy = 0$$

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This is separable: It can be rearranged to yield

$$\cos t dt = -\frac{e^y \sin y}{1 + e^y} dy$$

Integrating the right side is possible, but not so very nice.

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  • $\begingroup$ Yes, I did that but i was not able to take integral of right hand side. Mathematica did not give a simple result for integral of right hand side too. It was too long and complicated. $\endgroup$ Dec 17, 2013 at 1:21
  • $\begingroup$ Can you think an other, much simpler than integral of rhs, way? $\endgroup$ Dec 17, 2013 at 1:23
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    $\begingroup$ @OlcayErtaş I'd start by writing $\sin$ as a complex exponential or using $\sinh$ and $\cosh$. I don't see a way to get rid of the hypergeometric function. $\endgroup$
    – user61527
    Dec 17, 2013 at 1:23
  • $\begingroup$ Ok, thank you very much. $\endgroup$ Dec 17, 2013 at 1:24

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