Solve the differential equation. `(dy)/(dx) - y = e^(x)` Hence find the particluar solution for x = 0 and y = 1 .

Explanation

To solve the differential equation \(\frac{dy}{dx} - y = e^x\) and find the particular solution for \(x = 0\) and \(y = 1\), we will follow these steps:

### Step 1: Identify the form of the differential equation
The given equation can be rewritten as:
\[ \frac{dy}{dx} + (-1)y = e^x \]
This is in the standard form of a linear first-order differential equation:
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