Question

For the following differential equation verify that the accompanying function is a solution:

Differential equation	Function
\[x\frac{dy}{dx} = y\]	y = ax

Answer 1

We have,

\[y = ax ..............(1)\]

Given differential equation

\[x\frac{dy}{dx} = y\]

Differentiating both sides of (1) with respect to x, we get

\[\frac{dy}{dx} = a\]

\[ \Rightarrow \frac{dy}{dx} = \frac{y}{x} .........\left[\text{Using (1)}\right]\]

\[ \Rightarrow x\frac{dy}{dx} = y\]

Hence, the given function is the solution to the given differential equation.