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

  • question_answer
    The solution of the differential equation \[\frac{dy}{dx}=(1+x)(1+{{y}^{2}})\] is

    A)                 \[y=\tan ({{x}^{2}}+x+c)\]            

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

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

    D)                 \[y=\tan \left( \frac{{{x}^{2}}}{2}+x+c \right)\]

    Correct Answer: D

    Solution :

                       \[\frac{dy}{dx}=(1+x)(1+{{y}^{2}})\] Þ \[\frac{dy}{1+{{y}^{2}}}=(1+x)dx\]         On integrating both sides, we get                                 \[{{\tan }^{-1}}y=\frac{{{x}^{2}}}{2}+x+c\] Þ \[y=\tan \left( \frac{{{x}^{2}}}{2}+x+c \right)\].


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