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

  • question_answer
    Solution of differential equation \[\frac{dy}{dx}=2xy\]is [MP PET 1997]

    A)                 \[y=c{{e}^{{{x}^{2}}}}\]             

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

    C)                 \[y={{e}^{-{{x}^{2}}}}+c\]        

    D)                 \[y={{x}^{2}}+c\]

    Correct Answer: A

    Solution :

                       \[\int_{{}}^{{}}{\frac{dy}{y}=\int_{{}}^{{}}{2xdx}}\]Þ\[{{\log }_{e}}y={{x}^{2}}+c\]                 Þ \[y={{e}^{{{x}^{2}}+c}}={{e}^{c}}{{e}^{{{x}^{2}}}}\]Þ\[y=c{{e}^{{{x}^{2}}}}\].


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