Question
For the following differntial equations verify that the accompanying function is a solution:
Differential equation Function
$\text{x}\frac{\text{dy}}{\text{dx}}=\text{y}$ $\text{y}=\text{ax}$

Answer

We have
$\text{y}=\text{ax}\ ...(1)$
Given differential equation
Differentiating both sides of (1) with respect to x, we get
$\frac{\text{dy}}{\text{dx}}=\text{a}$
$\Rightarrow\frac{\text{dy}}{\text{dx}}=\frac{\text{y}}{\text{x}}$
$\Rightarrow\text{x}\frac{\text{dy}}{\text{dx}}={\text{y}}$
Hence, the given function is the solution to the given differential equation.

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