$$\frac{dy}{dx} = p \left( x \right) y + q \left( x \right)$$

**Procedure:**

**– Calculate $I = \int p\left( x \right) \, dx$**

**– Find the integrating factors $e^{-I \left( x \right)}$ and $e^{I \left( x \right)}$**

**– Evaluate $\int e^{I \left( x \right)} q \left( x \right) \, dx$**

**– Hence the solution:**

$$y = e^{-I \left( x \right)} \left( \int e^{I \left( x \right)} q \left( x \right) \, dx \right) + C e^{-I \left( x \right)}$$