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JEE Main & Advanced Mathematics Differential Equations Question Bank Formation of differential equations

  • question_answer
    The differential equation of the family of curves represented by the equation \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\] is

    A)                 \[x+y\frac{dy}{dx}=0\]      

    B)                 \[y\frac{dy}{dx}=x\]

    C)                 \[y\frac{{{d}^{2}}y}{d{{x}^{2}}}+{{\left( \frac{dy}{dx} \right)}^{2}}=0\]      

    D)                 None of these

    Correct Answer: A

    Solution :

               Given equation \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\]. Differentiate it w.r.t. x,                                 we get \[2x+2y\frac{dy}{dx}=0\] Þ \[x+y\frac{dy}{dx}=0\].


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