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JEE Main & Advanced Mathematics Differential Equations Question Bank Miscellaneous differential equations

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

    A)            \[\frac{1}{4}{{e}^{-2x}}\]  

    B)            \[\frac{1}{4}{{e}^{-2x}}+cx+d\]           

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

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

    Correct Answer: B

    Solution :

                       \[\frac{{{d}^{2}}y}{d{{x}^{2}}}={{e}^{-2x}}\]                    Integrating both sides, we get \[\frac{dy}{dx}=\frac{{{e}^{-2x}}}{-2}+c\]                    Again integrate, we get \[y=\frac{{{e}^{-2x}}}{4}+cx+d\].


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