The simplest type of differential equation

The simplest type of differential equation
The simplest ordinary of differential equation can be integrated directly by finding antiderivatives. These simplest odes have the form

Where the derivative of can be of any order and may depend only on the independent variable
Example 2:
Find the general solution of the differential equation
Then find the particular solution determined by the initial condition
Solution:





Example 3:
Find the particular solution of the differential equation determined by the initial conditions
Solution:







Example 4: Solve with
Solution:




1. Verify that is a solution for the differential equation

2. Verify that is a solution for the differential equation
Then find the particular solution determined by the initial condition

3. Solve with
4. Solve with
5. Find the particular solution for the differential equation determined by the initial conditions