Download presentation

Presentation is loading. Please wait.

Published byMarc Larry Modified over 3 years ago

1
CHAPTER 5 Higher-Order Linear Differntial Equations Second-order DE: Second-order linear DE: Note: A,B,C,F function of x only Second-order homogeneous linear DE: Note: F(x)=0 Second-order homogeneous linear DE (with constant coefficients): Note: A, B, C, are constants (all) (a,c,d,e) (d,e) (d)

2
CHAPTER 5 Higher-Order Linear Differntial Equations Second-order homogeneous linear DE: Note: F(x)=0 (d,e) are solutions ?? (verify) Consider the homogeneous 2ed-order linear DE: Let W = the set of all solutions of (*) (*) Let F = the set of all real-valued functions W is a subspace of F dim(W)=2

3
CHAPTER 5 Higher-Order Linear Differntial Equations Second-order homogeneous linear DE: Consider the homogeneous 2ed-order linear DE: (*) W is a subspace of F dim(W)=2 Give me other solutions???

4
CHAPTER 5 Higher-Order Linear Differntial Equations Consider the homogeneous 2ed-order linear DE: (*) How to solve homog. 2ed-order linear DE: 1 Find two linearly independent solutions for (*) 2 The general solution for (*)

5
CHAPTER 5 Higher-Order Linear Differntial Equations Consider the homogeneous 2ed-order linear DE (with constant coeff): (*) How to y1 & y2: 1 Find the characteristic equation Find the roots of (**) (**) 2 Distinct realrepeated real2 non-real

6
CHAPTER 5 Higher-Order Linear Differntial Equations Consider the homogeneous 2ed-order linear DE (with constant coeff): (*) How to y1 & y2: 1 Find the characteristic equation Find the roots of (**) (**) 2 Distinct realrepeated real2 non-real

7
CHAPTER 5 Higher-Order Linear Differntial Equations Consider the homogeneous 2ed-order linear DE (with constant coeff): (*) How to y1 & y2: 1 Find the characteristic equation Find the roots of (**) (**) 2 Distinct realrepeated real2 non-real

8
CHAPTER 5 Higher-Order Linear Differntial Equations Consider the homogeneous nth-order linear DE: (*) How to solve homog. nth-order linear DE: 1 Find n linearly independent solutions for (*) 2 The general solution for (*)

9
Consider the homogeneous nth-order linear DE (with constant coeff): How to y1, y2,.. yn: 1 Find the characteristic equation Find the roots of (**) (**) 2 Distinct realrepeated real non-real

10
Consider the homogeneous nth-order linear DE (with constant coeff): How to y1, y2,.. yn: 1 Find the characteristic equation Find the roots of (**) (**) 2 Distinct realrepeated real non-real

11
CHAPTER 5 Higher-Order Linear Differntial Equations Consider the homogeneous 2ed-order linear DE (with constant coeff): (*) How to y1 & y2: 1 Find the characteristic equation Find the roots of (**) (**) 2 Distinct realrepeated real2 non-real

12
Consider the homogeneous nth-order linear DE (with constant coeff): How to y1, y2,.. yn: 1 Find the characteristic equation Find the roots of (**) (**) 2 Distinct realrepeated real non-real

13
CHAPTER 5 Higher-Order Linear Differntial Equations Ploynomial Operator Write in operator form Euler’s Formula

14
CHAPTER 5 Higher-Order Linear Differntial Equations Consider the homogeneous nth-order linear DE: (*) How to solve homog. nth-order linear DE: 1 Find n linearly independent solutions for (*) The general solution for (*) 2 Consider the non-homogeneous nth-order linear DE: (**) How to solve non-homog. nth-order linear DE: 1 Solve the associated homog. DE (*) Find a particular solution for (**) 2 (complementary function) The general solution for (**) 3

15
CHAPTER 5 Higher-Order Linear Differntial Equations Consider the non-homogeneous nth-order linear DE: (**) How to solve homog. nth-order linear DE: 1 Solve the associated homog. DE (*) Find a particular solution for (**) 2 (complementary function) The general solution for (**) 3

Similar presentations

OK

Boyce/DiPrima 9th ed, Ch 4.2: Homogeneous Equations with Constant Coefficients Elementary Differential Equations and Boundary Value Problems, 9th edition,

Boyce/DiPrima 9th ed, Ch 4.2: Homogeneous Equations with Constant Coefficients Elementary Differential Equations and Boundary Value Problems, 9th edition,

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google