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

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

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

    B)                 \[y+\log (1+{{x}^{2}})+c=0\]

    C)                 \[y-\log (1+x)=c\]

    D)                 \[y={{\tan }^{-1}}x+c\]

    Correct Answer: D

    Solution :

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


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