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The general solution of the differential equation
$\mathrm{x} \frac{\mathrm{dy}}{\mathrm{dx}}+\mathrm{y}=0$ is?
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$\mathrm{x} \frac{\mathrm{dy}}{\mathrm{dx}}+\mathrm{y}=0$ is?
Solution:
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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 $\ell \mathrm{n} \mathrm{y}=-\ln \mathrm{x}+\mathrm{enc}$
$\Rightarrow\left(\mathrm{y}=\frac{\mathrm{c}}{\mathrm{x}}\right)$
$$
\mathrm{x} \frac{\mathrm{dy}}{\mathrm{dx}}+\mathrm{y}=0
$$
$\Rightarrow x d y+y d x=0$
$\Rightarrow x d y=-y d x$
$\Rightarrow \frac{\mathrm{dy}}{\mathrm{y}}=-\frac{\mathrm{dx}}{\mathrm{x}}$
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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