9.5 Differential Equations
Linear Equations: Overview
First Order Linear Differential Equation
First order linear differential equation is in the form of: ( ) ( ) where P and Q are
continuous functions over an interval.
First order differential equation means the highest order of derivative in the equation is first derivative.
Noting the form of product rule ( )
( )( ( ) ) ( ( ) ) if the integrating factor( ) can be found, then the equation becomes:
( ( ) ) ( ) ( ). Integrating both sides:( ) ∫ ( ) ( ) , then the solution is:
( ) ( )[∫ ( ) ( ) ]
∫ ( )
To find the integrating factor∫ ∫ ( ) ; | | ∫ (