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JEE Main & Advanced Mathematics Differential Equations Question Bank Homogeneous differential equations

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

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

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

    C)                 \[y+\sqrt{{{x}^{2}}+{{y}^{2}}}+c{{x}^{2}}=0\]               

    D)                 None of these

    Correct Answer: B

    Solution :

                    It is a homogenous equation, solve it by putting \[y=vx\]and \[\frac{dy}{dx}=v+x\frac{dv}{dx}\].


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