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

  • question_answer
    \[y=\frac{x}{x+1}\] is a solution of the differential equation

    A)                 \[{{y}^{2}}\frac{dy}{dx}={{x}^{2}}\]       

    B)                 \[{{x}^{2}}\frac{dy}{dx}={{y}^{2}}\]

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

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

    Correct Answer: B

    Solution :

                       \[y=\frac{x}{x+1}\Rightarrow \frac{1}{y}=1+\frac{1}{x}\]                                 \[-\frac{1}{{{y}^{2}}}\frac{dy}{dx}=0-\frac{1}{{{x}^{2}}}\] Þ \[{{x}^{2}}\frac{dy}{dx}={{y}^{2}}\].


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