Summary of Class 12 Maths Differential
Equations
An equation involving the dependent variable, independent variable
and the derivative(s) of the dependent variable with respect to independent
variable(s), is called a differential equation.
Ordinary Differential Equations
A differential equation involving derivatives of the dependent
variable with respect to only one independent variable is called an ordinary
differential equation.
Order of a Differential Equation
The order of a differential equation is the order of the highest
order derivative occurring in the differential equation.
Degree of a differential equation
The highest power (positive integral index) of the highest order
derivative occurring in differential equation, when it is written as a
polynomial in derivatives, is called the degree of the differential equation.
Solution of a Differential Equation
A function which satisfies the given differential equation is
called the solution of the differential equation.
There are many methods to solve differential equations.
General Solution of a Differential Equation
The solution of a differential equation which contains as many
arbitrary constants as the order of the differential equation, is called a
general solution of the differential equation.
Particular Solution of a Differential Equation
The solution obtained from the general solution by giving
particular values to the arbitrary constants is called a particular solution
of the differential equation.
Methods of Solving First Order and First Degree Differential Equations
1. Variable Separable Form
2. Homogeneous Differential Equations
3. Linear Differential Equations
A first order differential equation, in which the degree of
dependent variable and its derivative is one and they do not get multiplied
together, is called a linear differential equation.
