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  3. CEE Kerala Engineering

CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2008

  • question_answer
    The differential equation representing the family of curves\[{{y}^{2}}=2c(x+{{c}^{3}}),\]where c is a positive parameter, is of

    A)  order 1, degree 1           

    B)  order 1, degree 2

    C)  order 1, degree 3

    D)        order 1, degree 4

    E)  order 2, degree 1

    Correct Answer: D

    Solution :

    Given \[{{y}^{2}}=2cx+2{{c}^{4}}\] On differentiating w.r.t.\[x,\]we get \[2y\frac{dy}{dx}=2c\Rightarrow c=y\frac{dy}{dx}\] \[\therefore \]  \[{{y}^{2}}=2yx\frac{dy}{dx}+2{{\left( \frac{y\,dy}{dx} \right)}^{4}}\] Hence, order is 1 and degree is 4.


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