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Lecture

# 9.5 Linear Equations Overview

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Department
Mathematics
Course Code
MAT136H1
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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∫ ∫ ( ) ; | | ∫ (
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