The given first-order differential equation is:

\[
y' - \frac{y}{x} = x \cos x
\]

This is a linear first-order differential equation, and it can be solved using an **integrating factor**.

### Steps to solve:

1. **Rearrange the equation** in standard linear form:
   \[
   y' + P(x)y = Q(x)
   \]
   Here, we have:
   \[
   P(x) = -\frac{1}{x} \quad \text{and} \quad Q(x) = x \cos x
   \]

2. **Find

Explore how to solve the linear first-order differential equation y' - y/x = x cos x using the integrating factor method. This solution covers key concepts in differential equations and provides a step-by-step guide suitable for undergraduate mathematics students.

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