JEE Main & Advanced Mathematics Differential Equations Question Bank Self Evaluation Test - Differential Equations

  • question_answer
    What is the degree of the differential equation\[k\frac{{{d}^{2}}y}{d{{x}^{2}}}={{\left[ 1+{{\left( \frac{dy}{dx} \right)}^{3}} \right]}^{3/2}}\], where k is a constant?

    A) 1

    B) 2

    C) 3

    D) 4

    Correct Answer: B

    Solution :

    [b] In the given equation, \[K.\frac{{{d}^{2}}y}{d{{x}^{2}}}={{\left[ 1+{{\left( \frac{dy}{dx} \right)}^{3}} \right]}^{3/2}}\] Squaring both the sides, \[{{K}^{2}}.{{\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)}^{2}}={{\left[ 1+{{\left( \frac{dy}{dx} \right)}^{3}} \right]}^{3}}\] Degree of a differential equation is the highest power of the highest derivative in equation when derivatives are expressed as polynomial. Here degree of differential equation is 2.

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