MATH201 Lecture Notes - Lecture 8: Linear Combination, Ansatz
18 Jun 2015
School
Department
Course
Professor
Document Summary
Math 201 lecture 08 undetermined coefficients: how to solve homogeneous linear equations with constant coe cients, review, many examples here are taken from the textbook. The rst number in () refers to the problem number in the ua custom edition, the second number in () refers to the problem number in the 8th edition. C1 y1(t) + c2 y2(t) +(cid:10) + cn yn(t). of the equation), use them to get n equations for c1,(cid:9) , cn. Now arrange a list of roots with repeated roots grouped together and complex conjugates in pairs: To apply initial conditions, we prepare: quiz: We observe that r1 = 1 is a solution and factorize. Solving this system, we have c1 = c2 = c3 = 1. By now we have no problem getting y1, y2, which are linearly independent solutions to a y + b y + c y = 0. (16) (17) (18) (19) (20) (21)
