Q84 / 170 · Manipal (MET) 2017 · Mathematics

The differential equation of the family of lines passing through the origin is

  • A
    $x \frac{d y}{d x}+y=0$
  • B
    $x+\frac{d y}{d x}=0$
  • Correct answer
    C
    $x \frac{d y}{d x}-y=0$
  • D
    $\frac{d y}{d x}=x$

Solution

The equation of line passing through the origin is given by $y=m x...(i)$ On differentiating w.r.t. $x$, we get $\begin{array}{ll} & \frac{d y}{d x}=m \Rightarrow \frac{d y}{d x}=\frac{y}{x} \quad \text { [from Eq. (i)] } \\ \Rightarrow & x \frac{d y}{d x}-y=0 \end{array}$

Hence, the correct answer is option: 'C'.

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