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  3. CEE Kerala Engineering

CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2002

  • question_answer
    The differential equation of the family of lines passing through the origin is:

    A)  \[x\frac{dy}{dx}+y=0\]                

    B)                         \[x+\frac{dy}{dx}=0\]

    C)                         \[\frac{dy}{dx}=y\]                       

    D)                         \[\frac{dy}{dx}=x\]

    E)                         \[x\frac{dy}{dx}-y=0\]

    Correct Answer: E

    Solution :

    The equation of line passing through the origin is given by \[y=mx\]                                            ...(i) On differentiating w.r.t.\[x,\]we get                 \[\frac{dy}{dx}=m\] \[\Rightarrow \]               \[\frac{dy}{dx}=\frac{y}{x}\] (using Eq. (i)) \[\Rightarrow \]               \[x\frac{dy}{dx}-y=0\]


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