MAT136H1 Lecture Notes - Inductor, Integrating Factor, Product Rule

• School: UTSG
• Department: Mathematics
• Course: MAT136H1
• Professor: all

Document Summary

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: ( ) ; | | ( ) ; raising to power: ( ) , To find the integrating factor: where , but since a particular integrating factor is needed and not a general expression, Kirchhoff"s law gives the relationship ( ), where is the voltage drop across the capacitor. , which is the current at time , then the equation can be written as ( ) which is in the form of linear differential equation.