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JEE Main & Advanced AIEEE Solved Paper-2002

  • question_answer
    The solution of the equation \[\frac{{{d}^{2}}y}{d{{x}^{2}}}={{e}^{-2x}}\] is   AIEEE  Solved  Paper-2002

    A)      \[\frac{{{e}^{-2x}}}{4}\]                   

    B)                     \[\frac{{{e}^{-2x}}}{4}\,+cx+d\]

    C) \[\frac{1}{4}{{e}^{-2x}}+c\,{{x}^{2}}+d\]

    D)           \[\frac{1}{4}{{e}^{-2x}}+c\,+d\]

    Correct Answer: B

    Solution :

                            Since,       \[\frac{{{d}^{2}}y}{d{{x}^{2}}}={{e}^{-2x}}\] On integrating both sides, we get \[\Rightarrow \]   \[\frac{dy}{dx}=\frac{{{e}^{-2x}}}{-2}+c\] Again integrating, \[y=\frac{{{e}^{-2x}}}{4}+cx+d\]


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