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JEE Main & Advanced Mathematics Differential Equations Question Bank Critical Thinking

  • question_answer
    The degree of the differential equation \[3\frac{{{d}^{2}}y}{d{{x}^{2}}}={{\left\{ 1+{{\left( \frac{dy}{dx} \right)}^{2}} \right\}}^{3/2}}\] is [MP PET 1994, 95]

    A) 1    

    B) 2

    C) 3    

    D) 6

    Correct Answer: B

    Solution :

    • \[3\frac{{{d}^{2}}y}{d{{x}^{2}}}={{\left\{ 1+{{\left( \frac{dy}{dx} \right)}^{2}} \right\}}^{3/2}}\]        
    • On squaring, we get \[9{{\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)}^{2}}={{\left\{ 1+{{\left( \frac{dy}{dx} \right)}^{2}} \right\}}^{3}}\]           
    • Obviously the highest derivative \[\frac{{{d}^{2}}y}{d{{x}^{2}}}\] contains a degree 2.


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