N-th order linear DE

1. CH 6: Series Solutions of Linear Equations N-th order linear DE Constant Coeff variable Coeff Cauchy-Euler 4.7 In General Ch 6 Power Series Homog(findyp) 4.3 NON-HOMOG (find yp) Annihilator Approach 4.5 Variational of Parameters 4.6

2. WED

3. star

4. Sec 6.2: Solution about Ordinary Points Find two power series solutions of the given differential equation about the point x=0

5. Ordinary Points Definition: Is analytic at IF: Can be represented by power series centerd at (i.e) with R>0 Definition: Is an ordinary point of the DE (*) IF: are analytic at A point that is not an ordinary point of the DE(*) is said to be singular point

6. Ordinary Points Definition: Is an ordinary point of the DE (*) IF: are analytic at A point that is not an ordinary point of the DE(*) is said to be singular point Special Case: Polynomial Coefficients

7. Ordinary Points Special Case: Polynomial Coefficients

8. Existence of Power series Solutions Theorem 6.1: Existence of Power Series Solutions IF is an ordinary point ? X=0 is an ordinary point . We can find 2-lin-indep sol in the form

9. Existence of Power series Solutions Theorem 6.1: Special case IF is an ordinary point