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JEE Main & Advanced Mathematics Differential Equations Question Bank Order and degree of differential equations

  • question_answer
    The order and degree of the differential equation \[{{\left[ 4+{{\left( \frac{dy}{dx} \right)}^{2}} \right]}^{2/3}}=\frac{{{d}^{2}}y}{d{{x}^{2}}}\] are

    A)                 2, 2         

    B)                 3, 3

    C)                 2, 3         

    D)                 3, 2

    Correct Answer: C

    Solution :

                       Here power on the differential coefficient is fractional, therefore change it into positive integer, so                    \[{{\left[ 4+{{\left( \frac{dy}{dx} \right)}^{2}} \right]}^{2/3}}=\frac{{{d}^{2}}y}{d{{x}^{2}}}\] Þ \[{{\left[ 4+{{\left( \frac{dy}{dx} \right)}^{2}} \right]}^{2}}={{\left[ \frac{{{d}^{2}}y}{d{{x}^{2}}} \right]}^{3}}\]                                 Hence order is 2 and degree is 3.


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