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KVPY Sample Paper KVPY Stream-SX Model Paper-30

  • question_answer
    If p and q are order and degree of differential equation \[{{y}^{2}}{{\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)}^{2}}+3x{{\left( \frac{dy}{dx} \right)}^{1/3}}+{{x}^{2}}{{y}^{2}}=\sin \,x\], then:

    A) \[p>q\]

    B) \[\frac{p}{q}=\frac{1}{2}\]

    C) \[p=q\]

    D) \[p<q\]

    Correct Answer: D

    Solution :

    \[{{y}^{2}}{{\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)}^{2}}+{{x}^{2}}{{y}^{2}}-\sin x=-3x{{\left( \frac{dy}{dx} \right)}^{1/3}}\]
    \[{{\left( {{y}^{2}}{{\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)}^{2}}+{{x}^{2}}{{y}^{2}}-\sin x \right)}^{3}}=-9{{x}^{3}}\left( \frac{dy}{dx} \right)\]
    Here order = 2 = p
    Degree = 6 = q              \[\therefore \]      \[p<q\]


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