Question

In each of Problems 1 through 3, use the method of variation of parameters to find a particular solution of the given differential equation. Then check your answer by using the method of undetermined coefficients. 1. y" - 5y + 6y - 2 ANSWER O Y(A) = 2. y - y - 2y - 2e? ANSWER WORKED SOLUTION 2.4" - 4y + y - 16/2

Answer 1

- 2 et m2- Smt = ° M (m-2-3 (m-2) m2 3, m-2 0 Ge ue, v ze3* R=2 et e 2 e2t 3 e3 A 3 et2 e = 3t 2 et A - 2 est A 2e t u e2t 2et e st feu 2. - e 2t -t Aut Bv (-2et 2 etet et DircatPartica Tnteqoal, 1 2 et 2. m2- 2 m+m 20 M(m- 2+ (m-2)20 ma m2 e27 e 2 et et3et -e 2e

A3 e2tx 2edt 3 et A dr 3et 3t -3t -2 te -3t 2 e AuRv j 글바 e-t 2 ( 2. et D- D- 2 2 e t D+ (D-2 J 2t (D+1) 3 (D-2) । ৫) 3 D+1) -2 +2 -2 et D-1 e

4-4yt1e 4m-4mt1 - ° 4m2-2 m-2m +1= ° 2 m(2m1 (rm-1)30 (2m- m о с.Е Сer+ ctie сеч+ Cate th Ивеth, Vз teth w e e th , t/ е е е е е te e t 6 e А- - А в -16 t е % 16eth В- e t Hе 16t Рт, Y(4)- Au + Bv t2eth -16 te th 2.

D'reat Partiaular Inhegal i 6 e 4D2-4D 16 etA 4et D-J 2 D-2 4 e D*V- yeth 2t2et