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

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

    A)                 \[x+y+\tan (x+c)=0\]         

    B)                 \[x-y+\tan (x+c)=0\]

    C)                 \[x+y-\tan (x+c)=0\]           

    D)                 None of these

    Correct Answer: C

    Solution :

                       Put \[x+y=v\]and \[1+\frac{dy}{dx}=\frac{dv}{dx}\]                    Þ \[\frac{dv}{dx}={{v}^{2}}+1\]Þ\[\frac{dv}{{{v}^{2}}+1}=dx\]                    On integrating, we get                                 \[{{\tan }^{-1}}v=x+c\]or \[v=\tan (x+c)\] Þ\[x+y=\tan (x+c)\].


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