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Question
For the following differential equation verify that the accompanying function is a solution:
| Differential equation | Function |
|
\[x\frac{dy}{dx} = y\]
|
y = ax |
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Solution
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.
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