# First Order Linear Differential Equations

First Order Linear Differential Equations

First Order Homogeneous Linear Differential Equations

### Solving First Order Linear Differential Equations

A differential equation that can be written in the following form is called first order linear differential equation:

In order to solve linear differential equations we will set:

The solution of the linear differential equation is given by the formula:

**Example 1:**

First step:

*Second step:

The solution is:

**More information about integration calculations in the menu Mathematics/Integration/Methods.*

**Example 2:**

First step:

*Second step:

The solution is:

**More information about integration calculations in the menu Mathematics/Integration/Methods.*

**Example 3:**

First step:

*Second step:

The solution is:

**More information about integration calculations in the menu Mathematics/Integration/Methods.*

### Solving First Order Homogeneous Linear Differential Equations

A homogeneous linear differential equation is similar to linear differential equation except that Q(x) is equal to zero:

The solution of the homogeneous case is:

**Example:**