Page 4 - CH 9 Differential Equation Lession Notes

Integrating both sides, we get,

v + logx = c

is the required solution.

9.5.3 Linear differential equations

A differential equation of the from

where, P and Q are constants or functions of x only, is known as a first order linear differential
equation.

Steps involved to solve first order linear differential equation:
Find the Integrating Factor
Write the solution of the given differential equation as
As ( ) ( )

A differential equation of the from

where, P and Q are constants or functions of y only, is known as a first order linear differential
equation.

Steps involved to solve first order linear differential equation:
Find the Integrating Factor
Write the solution of the given differential equation as
As ( ) ( )

Example: Solve the following differential equation:

Sol :

Therefore, integrating factor (IF) =
Therefore,

-1
Putting t = tan x, we get

Therefore,