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CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2011

  • question_answer
    The general solution of the differential equation\[\frac{dy}{dx}={{e}^{y}}({{e}^{x}}+{{e}^{-x}}+2x)\]is

    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                 \[-{{e}^{-y}}={{e}^{x}}-{{e}^{-x}}+{{x}^{2}}-C\] \[\Rightarrow \]               \[{{e}^{-y}}={{e}^{-x}}-{{e}^{x}}-{{x}^{2}}+C\]


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