JEE Main & Advanced Mathematics Differential Equations Question Bank Variable Separable type differential equations

  • question_answer
    The solution of \[\frac{dy}{dx}=x\log x\]is       [MP PET 2003]

    A)                 \[y={{x}^{2}}\log x-\frac{{{x}^{2}}}{2}+c\]           

    B)                 \[y=\frac{{{x}^{2}}}{2}\log x-{{x}^{2}}+c\]

    C)                 \[y=\frac{1}{2}{{x}^{2}}+\frac{1}{2}{{x}^{2}}\log x+c\]   

    D)                 None of these

    Correct Answer: D

    Solution :

                       \[\frac{dy}{dx}=x\log x\] Þ \[dy=x\log xdx\]                                 Þ \[\int_{{}}^{{}}{dy=}\int_{{}}^{{}}{x\log xdx}\]Þ \[y(0)=0\].


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