An equation involving derivatives with only one variable is an Ordinary Differential Equation.
An equation involving derivatives with more than one variable is a Partial Differential Equation.
Order:
The order of the Ordinary differential equation is the order of a higher-order derivative involved in the ordinary differential equation.
Degree:
The degree of the Ordinary differential equation is the highest power of the higher-order derivative after it is free from radicals and fractions.
Order = 2
Degree = 1
Linear differential equation:
An Ordinary differential equation is called linear if 'y' is a dependent variable then powers of 
should be 1 and all of these should not
multiply with each other.
A standard form of nth order differential equation is
The equations which do not satisfy these conditions are called non-linear differential equations.
Example 1:
The order for this equation is 2 and the degree is 2. This is a non-linear differential equation.
Any relation satisfying differential equation is called a solution.
The general solution is a linear combination of linearly independent solutions.
In general solution, the number of arbitrary constants is equal to the order of a differential equation.
A particular solution is if we assign particular values in place of arbitrary constants of a general solution. The resulting solution is called a particular solution.
Solution of first-order first-degree differential equation:
A first-order and first-degree differential equation may be in the following forms.
- Variable separable form
- Exact differential equation
- Linear differential equation
- Homogeneous differential equation
then the differential equation is said to be in the variable separable form.
