A) \[{{e}^{-y}}={{e}^{x}}-{{e}^{-x}}+{{x}^{2}}+C\]
B) \[{{e}^{-y}}={{e}^{-x}}-{{e}^{x}}-{{x}^{2}}+C\]
C) \[{{e}^{-y}}=-{{e}^{-x}}-{{e}^{x}}-{{x}^{2}}+C\]
D) \[{{e}^{y}}={{e}^{-x}}+{{e}^{x}}+{{x}^{2}}+C\]
E) \[{{e}^{y}}={{e}^{-x}}+{{e}^{x}}+C\]
Correct Answer: B
Solution :
\[\frac{dy}{dx}={{e}^{y}}({{e}^{x}}+{{e}^{-x}}+2x)\] \[\Rightarrow \] \[{{e}^{-y}}dy=({{e}^{x}}+{{e}^{-x}}+2x)dx\] On integrating \[-{{e}^{-y}}={{e}^{x}}-{{e}^{-x}}+{{x}^{2}}-C\] \[\Rightarrow \] \[{{e}^{-y}}={{e}^{-x}}-{{e}^{x}}-{{x}^{2}}+C\]You need to login to perform this action.
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