MATH201 Lecture Notes - Lecture 9: Integrating Factor

• School: University of Alberta
• Department: Mathematics
• Course: MATH201
• Professor: Mohammad Ali Niksirat

Document Summary

Math201(lecture 9): differential equation: exact equations ( cont"d) If , find the integrating factor such that the equation. Solution: (a) check for exactness: (b) find an integrating factor that depends only on one variable: If depends only on y, then: (c) multiply integrating factor on both sides of given equation and test for exactness. If exact, solve using the exact equation method. Note: no integration technique exists for the general 2nd order des. Note: no general integration techniques for the general linear des. We consider (mainly) equations with , are constant functions. If function r(x) is the right hand side of (*) is called forcing term. If r=0, the equation is called 2nd order linear homogeneous equation with constant coefficient. Superposition property: (1) the solution to the equation (*), is written as where is called the homogeneous solution to the equation. 22nd order de and is called a particular solution to the equation (*)