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

  • question_answer
    If m and n are the order and degree of the differential equation \[{{\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)}^{5}}+4\frac{{{\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)}^{3}}}{\left( \frac{{{d}^{3}}y}{d{{x}^{3}}} \right)}+\frac{{{d}^{3}}y}{d{{x}^{3}}}={{x}^{2}}-1\], then [Karnataka CET 1999]

    A)                 m = 3 and n = 5

    B)                 m = 3 and n = 1

    C)                 m = 3 and n = 3      

    D)                 m = 3 and n = 2

    Correct Answer: D

    Solution :

                    The highest order \[(m)\] of the given equation is \[\frac{{{d}^{3}}y}{d{{x}^{3}}}=3\] and degree \[(n)\] of the given equation is \[{{\left( \frac{{{d}^{3}}y}{d{{x}^{3}}} \right)}^{2}}=2\]. Therefore \[m=3\] and \[n=2\].


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