Great! The equation is:

\[
y'' - y = e^x
\]

To solve this differential equation using the **method of variation of parameters**, we proceed with the following steps:

### Step 1: Solve the Homogeneous Equation

First, solve the associated homogeneous equation:

\[
y'' - y = 0
\]

The characteristic equation corresponding to this differential equation is:

\[
r^2 - 1 = 0
\]

Solving for \(

Explore how to solve the differential equation y'' - y = e^x using the method of variation of parameters. This problem covers advanced topics in differential equations and parameter variation. Suitable for advanced undergraduate students.

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