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

  • question_answer
    What is the degree of the differential equation\[{{\left( \frac{{{d}^{3}}y}{d{{x}^{3}}} \right)}^{2/3}}+4-3\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)+5\left( \frac{dy}{dx} \right)=0\]?

    A) 3

    B) 2

    C) 2/3

    D) Not defined

    Correct Answer: B

    Solution :

    [b] Degree of a differential equation is the power to which the highest derivative is raised when it is expressed as polynomial of derivatives. Given equation is \[{{\left( \frac{{{d}^{3}}y}{d{{x}^{3}}} \right)}^{2/3}}-3\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)+5\left( \frac{dy}{dx} \right)+4=0\] \[\Rightarrow {{\left( \frac{{{d}^{3}}y}{d{{x}^{3}}} \right)}^{2/3}}=3\frac{{{d}^{2}}y}{d{{x}^{2}}}-5\frac{dy}{dx}-4\] Cube on both side. \[{{\left( \frac{{{d}^{3}}y}{d{{x}^{3}}} \right)}^{2}}={{\left[ 3\frac{{{d}^{2}}y}{d{{x}^{2}}}-5\frac{dy}{dx}-4 \right]}^{3}}\] Hence, degree = 2

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