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: