An equation consisting of a differential coefficient is called a differential equation.
LDE has many applications in engineering problems.
is the differential equation.
A differential equation of the form
is known as a linear differential equation or simply LDE.
P and Q, are functions of x or constants.
The solution of LDE is-
2. If the RHS of LDE is zero for all x then it is said to be homogeneous, otherwise non-homogeneous.
Solving a linear differential equation
1. First change the given equation to the standard form of LDE, which is
2. Find the integrating factor
3. Then the solution of LDE is-
First we will convert the given equation in standard LDE form-
Where Q = sin x and P = 2/x
Now we will find the integrating factor-
Then the solution is-
Integrating by parts-
The given equation is already in the form of standard LDE.
Now we will find the IF-
So that the solution is-