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JCECE Engineering JCECE Engineering Solved Paper-2015

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

    A) \[m=3,\,\,n=3\]                               

    B) \[m=3,\,\,n=2\]

    C) \[m=3,\,\,n=5\]                               

    D)  \[m=3,\,\,n=1\]

    Correct Answer: B

    Solution :

    The given differential equation can be written as \[\left( \frac{{{d}^{3}}y}{d{{x}^{3}}} \right)-({{x}^{2}}-1)\frac{{{d}^{3}}y}{d{{x}^{3}}}+\left( \frac{{{d}^{3}}y}{d{{x}^{3}}} \right){{\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)}^{5}}+4\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)=0\]Clearly, its order is 3 and degree is 2.                 \[m=3\]and\[n=2\]


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