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JEE Main & Advanced Mathematics Differential Equations Question Bank Self Evaluation Test - Differential Equations

  • question_answer
    A curve passing through (2, 3) and satisfying the differential equation \[\int_{0}^{x}{ty(t)dt={{x}^{2}}y(x),(x>0)}\] is

    A) \[{{x}^{2}}+{{y}^{2}}=13\]

    B) \[{{y}^{2}}=\frac{9}{2}x\]

    C) \[\frac{{{x}^{2}}}{8}+\frac{{{y}^{2}}}{18}=1\]

    D) \[xy=c\]

    Correct Answer: D

    Solution :

    [d] Differentiate \[xy(x)={{x}^{2}}y'(x)+2xy(x)\] or \[xy(x)+{{x}^{2}}y'(x)=0\]   or \[x\frac{dy}{dx}+y=0\] or \[ln\,\,y+ln\,\,x=ln\,\,c\]          or \[xy=c\]


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