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

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

    A)                 \[{{x}^{3}}-{{y}^{3}}=c\]           

    B)                 \[{{x}^{3}}+{{y}^{3}}=c\]

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

    D)                 \[{{x}^{2}}-{{y}^{2}}=c\]

    Correct Answer: A

    Solution :

                       We have \[{{y}^{2}}dy={{x}^{2}}dx\]                 Integrating, we get\[{{y}^{3}}-{{x}^{3}}=c\]Þ \[{{x}^{3}}-{{y}^{3}}=c\].


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