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  4. The D.E whose solution is y = cx2 is

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Q. The D.E whose solution is $y = cx^2$ is

Differential Equations

Solution:

$y = cx^{2} \quad\ldots\left(1\right)$
$\Rightarrow \frac{dy}{dx} = 2cx$
$\Rightarrow \frac{dy}{dx} = 2\left(\frac{y}{x^{2}}\right)x \,\because$ from $\left(1\right)$
$\Rightarrow x \frac{dy}{dx} = 2y$