Ordinary differential equations, examples, types and solving methods
In solving different ordinary differential equations, it might be necessary to do various operations and use integration techniques in order to obtain the solution.
A differential equation which contains derivatives with respect to only one variable is known as ordinary differential equation. Basically, the differential equations which contain are named first order differential equations. Also, the differential equation which contain is called second order differential equations, and so on the differentials are known as higher order differential equations.
Ordinary differentials vary very much from one to other. They might be of any order and of any degree. The order of a differential equation is given by the derivative which has been differentiated the most. In order to determine the degree of a differential equation, we firstly have to check if it is a polynomial equation in y' or its higher order. If yes, than the degree we are looking for is given by the highest power of the highest order. If the equation is not a polynomial one, then the degree is not defined.
The ordinary differential equations divide in three categories:
1.) Separable Differential Equations
2.) Homogeneous Differential Equations
3.) Linear Differential Equations.
We will have a more detailed look at the last type of equations. A differential equation which has the following form: is known as a linear differential equation, as long as P and Q are only functions of x or constant, or only functions of y and constants.
Lets start solving ordinary differential equations
In order to solve a linear differential equation, you have to base on the concept of product rule of differentiation. The method could seem really complicated, but a solved example might clarify the problem for you.
Let's see some ordinary differential equations examples
You must have a general idea of how ordinary differential equations look like, this is why we provide you a series of ordinary differential equation examples:
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