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NDA 2012
Exam
NDA
Year
2012
Subject
Mathematics
Chapter
Differential Equations

NDA 2012 · Mathematics · Differential Equations

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

What is the solution of the differential equation dydx+yx=0\frac{d y}{d x}+\frac{y}{x}=0 ? where cc is a constant.

Options

  1. Axy=cx y=c
  2. Bx=cyx=c y
  3. Cy=cxy=c x
  4. DNone of the above

Correct answer

A. xy=cx y=c

Step-by-step solution

dydx=−yxdyy=−dxxdyy+dxx=0integration log⁡y+log⁡x=log⁡1+log⁡Clog⁡xy=log⁡(1.c)xy=c\begin{aligned} & \frac{d y}{d x}=\frac{-y}{x} \\ & \frac{d y}{y}=-\frac{d x}{x} \quad \frac{d y}{y}+\frac{d x}{x}=0 \\ & \text{integration } \\ & \log y+\log x=\log 1+\log \mathrm{C} \\ & \log x y=\log (1. c) \\ & x y=c\end{aligned}
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