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JEE Main & Advanced Mathematics Differential Equations Question Bank Application of differnetial equations

  • question_answer
    The differential equation \[y\frac{dy}{dx}+x=a\](a is any constant) represents

    A)                 A set of circles having centre on the y-axis

    B)                 A set of circles centre on the x-axis

    C)                 A set of ellipses

    D)                 None of these

    Correct Answer: B

    Solution :

                       We have \[y\frac{dy}{dx}+x=a\]or\[ydy+xdx=adx\]         Integrating, we get \[\frac{{{y}^{2}}}{2}+\frac{{{x}^{2}}}{2}=ax+c\]         or \[{{x}^{2}}+{{y}^{2}}-2ax+k=0\],                                 which represents a set of circles having centre on x-axis.


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