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JEE Main & Advanced AIEEE Solved Paper-2003

  • question_answer
    The degree and order of the differential equation of the family of all parabolas whose axis is X-axis, are respectively     AIEEE  Solved  Paper-2003

    A)                                         2, 1        

    B)       1, 2        

    C)       3, 2        

    D)       2, 3

    Correct Answer: B

    Solution :

    General equation of parabola whose axis is X-axis, is                                     \[{{y}^{2}}=4a(x+h)\] On differentiating w.r.t. x, we get                     \[2y\frac{dy}{dx}=4a\] \[\Rightarrow \]   \[y=\frac{dy}{dx}=2a\] Again, differentiating w.r.t. x, we get                                 \[y{{\left( \frac{dy}{dx} \right)}^{2}}+y\frac{{{d}^{2}}y}{d{{x}^{2}}}=0\] This is a differential equation whose degree and order are 1 and 2, respectively.


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