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$y=\mathrm{A} x \quad: \quad x y^{\prime}=y(x \neq 0)$


$y=\mathrm{A} x$

Differentiating both sides with respect to x, we get:

$y^{\prime}=\frac{d}{d x}(\mathrm{Ax})$

$\Rightarrow y^{\prime}=\mathrm{A}$

Substituting the value ofin the given differential equation, we get:

L.H.S. $=x y^{\prime}=x \cdot \mathrm{A}=\mathrm{A} x=y=$ R.H.S.

Hence, the given function is the solution of the corresponding differential equation.

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