Q241 / 270 · NDA 2019 (Phase 1) · Mathematics

What is the general solution of the differential equation $\frac{d y}{d x}+\frac{x}{y}=0$ ?

  • Correct answer
    A
    $\mathrm{x}^2+\mathrm{y}^2=\mathrm{c}$
  • B
    $\mathrm{x}^2-\mathrm{y}^2=\mathrm{c}$
  • C
    $\mathrm{x}^2+\mathrm{y}^2=\mathrm{cxy}$
  • D
    $x+y=c$

Solution

$\frac{d y}{d x}+\frac{x}{y}=0$ $\begin{aligned} & \Rightarrow \frac{d y}{d x}=\frac{-x}{y} \\ & \Rightarrow y d y+x d x=0 \\ & \Rightarrow \frac{y^2}{2}+\frac{x^2}{2}+c=0 \\ & \Rightarrow y^2+x^2+2 c=0 \\ & \Rightarrow x^2+y^2=c\end{aligned}$

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

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