JEE Main & Advanced Mathematics Differential Equations Question Bank Formation of differential equations

  • question_answer
    The differential equation of all straight lines passing through the origin is [DCE 2002; Kerala (Engg.) 2002; UPSEAT 2004]

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

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

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

    D)                 None of these

    Correct Answer: C

    Solution :

                       The equation of all straight lines passing through the origin is \[y=mx\]                                    .?.(i)                    where m is arbitrary constant         Differentiate (i) w.r.t. x, we get                                 \[\frac{dy}{dx}=m\] Þ \[\frac{dy}{dx}=\frac{y}{x}\],                   (By (i)).


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