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JEE Main & Advanced Mathematics Differential Equations Question Bank Critical Thinking

  • question_answer
    The order and degree of the differential equation \[{{\left( 1+3\frac{dy}{dx} \right)}^{\frac{2}{3}}}=4\frac{{{d}^{3}}y}{d{{x}^{3}}}\] are [AIEEE 2002]

    A) \[1,\,\frac{2}{3}\]                    

    B) 3, 1

    C) 3, 3

    D) 1, 2

    Correct Answer: C

    Solution :

    • To check, order and degree, the given differential equation should be free from radicals, hence taking cube on both sides, \[{{\left( 1+3.\frac{dy}{dx} \right)}^{2}}={{\left( 4.\frac{{{d}^{3}}y}{d{{x}^{3}}} \right)}^{3}}\]                   
    • Clearly, order = 3, degree = 3.


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