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  4. The general solution of the differential equation (dy/dx)=ey(ex+e-x+2x) is

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Q. The general solution of the differential equation $ \frac{dy}{dx}={{e}^{y}}({{e}^{x}}+{{e}^{-x}}+2x) $ is

KEAMKEAM 2011

Solution:

$ \frac{dy}{dx}={{e}^{y}}({{e}^{x}}+{{e}^{-x}}+2x) $
$ \Rightarrow $ $ {{e}^{-y}}dy=({{e}^{x}}+{{e}^{-x}}+2x)dx $
On integrating $ -{{e}^{-y}}={{e}^{x}}-{{e}^{-x}}+{{x}^{2}}-C $
$ \Rightarrow $ $ {{e}^{-y}}={{e}^{-x}}-{{e}^{x}}-{{x}^{2}}+C $