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NDA 2019
Exam
NDA
Year
2019
Subject
Mathematics
Chapter
Differential Equations

NDA 2019 · Mathematics · Differential Equations

What is the general solution of the differential equation (d y)/(d...

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

Options

  1. Ax2+y2=c\mathrm{x}^2+\mathrm{y}^2=\mathrm{c}
  2. Bx2−y2=c\mathrm{x}^2-\mathrm{y}^2=\mathrm{c}
  3. Cx2+y2=cxy\mathrm{x}^2+\mathrm{y}^2=\mathrm{cxy}
  4. Dx+y=cx+y=c

Correct answer

A. x2+y2=c\mathrm{x}^2+\mathrm{y}^2=\mathrm{c}

Step-by-step solution

dydx+xy=0\frac{d y}{d x}+\frac{x}{y}=0⇒dydx=−xy⇒ydy+xdx=0⇒y22+x22+c=0⇒y2+x2+2c=0⇒x2+y2=c\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}$$
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