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

  • question_answer
    The solution of the differential equation \[\frac{{{d}^{2}}y}{d{{x}^{2}}}=-\frac{1}{{{x}^{2}}}\]  is [MP PET 2003]

    A)            \[y=\log x+{{c}_{1}}x+{{c}_{2}}\]                                      

    B)            \[y=-\log x+{{c}_{1}}x+{{c}_{2}}\]

    C)            \[y=-\frac{1}{x}+{{c}_{1}}x+{{c}_{2}}\]                          

    D)            None of these

    Correct Answer: A

    Solution :

                       \[\frac{{{d}^{2}}y}{d{{x}^{2}}}=-\frac{1}{{{x}^{2}}}\]. Now integrating both sides, we get            \[\frac{dy}{dx}=\frac{1}{x}+{{c}_{1}}\] Þ \[y=\log x+{{c}_{1}}x+{{c}_{2}}\].


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