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Question: Answered & Verified by Expert
The general solution of the differential equation
$\mathrm{x} \frac{\mathrm{dy}}{\mathrm{dx}}+\mathrm{y}=0$ is?
MathematicsDifferential EquationsNDANDA 2013 (Phase 1)
Options:
  • A $x y=c$
  • B $\mathrm{x}=\mathrm{cy}$
  • C $x+y=c$
  • D $x^{2}+y^{2}=c$
Solution:
2737 Upvotes Verified Answer
The correct answer is: $x y=c$
Given differential equation is
$$
\mathrm{x} \frac{\mathrm{dy}}{\mathrm{dx}}+\mathrm{y}=0
$$
$\Rightarrow x d y+y d x=0$
$\Rightarrow x d y=-y d x$
$\Rightarrow \frac{\mathrm{dy}}{\mathrm{y}}=-\frac{\mathrm{dx}}{\mathrm{x}}$
On integrating both side we get $\ell \mathrm{n} \mathrm{y}=-\ln \mathrm{x}+\mathrm{enc}$
$\Rightarrow\left(\mathrm{y}=\frac{\mathrm{c}}{\mathrm{x}}\right)$

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