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What is the solution of the differential equation
$\frac{y d x-x d y}{y^{2}}=0 ?$
Options:
$\frac{y d x-x d y}{y^{2}}=0 ?$
Solution:
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Verified Answer
The correct answer is:
$y=c x$
$\frac{y \mathrm{dx}-\mathrm{x} \mathrm{dy}}{\mathrm{y}^{2}}=0$
$\therefore \quad y d x-x d y=0$
$\therefore \quad \frac{d y}{y}=\frac{d x}{x}$
Now integrating both sides,
$\int \frac{\mathrm{dy}}{\mathrm{y}}=\int \frac{\mathrm{dx}}{\mathrm{x}}$
$\Rightarrow \log y=\log x+\log c$
$\Rightarrow \log \mathrm{y}=\log \mathrm{c} \mathrm{x}$
$\mathrm{y}=\mathrm{cx}$
$\therefore$ Option (b) is correct.
$\therefore \quad y d x-x d y=0$
$\therefore \quad \frac{d y}{y}=\frac{d x}{x}$
Now integrating both sides,
$\int \frac{\mathrm{dy}}{\mathrm{y}}=\int \frac{\mathrm{dx}}{\mathrm{x}}$
$\Rightarrow \log y=\log x+\log c$
$\Rightarrow \log \mathrm{y}=\log \mathrm{c} \mathrm{x}$
$\mathrm{y}=\mathrm{cx}$
$\therefore$ Option (b) is correct.
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