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NDA 2013
Exam
NDA
Year
2013
Subject
Mathematics
Chapter
Differential Equations

NDA 2013 · Mathematics · Differential Equations

The general solution of the differential equation x (d y)/(d x)+y=0...

The general solution of the differential equation x \frac{d y}{d x}+y=0 \text{ is }wherewherecisanorbitraryconstant.is an orbitrary constant.

Options

  1. Axy=cx y=c
  2. Bx=cyx=c y
  3. Cx+y=cx+y=c
  4. Dx2+y2=cx^2+y^2=c

Correct answer

A. xy=cx y=c

Step-by-step solution

dyy=−dxxln⁡y=−ln⁡x+ln⁡c\lleft(y=cx)\frac{d y}{y}=-\frac{d x}{x}\ln y=-\ln x+\ln c \l left(y=\frac{c}{x})
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