Question

1. i) Find a particular solution by undetermined coefficients. ii) Find a particular solution by variation of parameters. iii) Are the answers the same? If not, what is the difference? (h) y" – y = 32.7231

Answer 1

у". y = 0 Put y'=m +2 1 => | m {m - 11 х Ciet Ce . Ус = Зх. Ур (A + в) 31 3 Ае Yp' у 31 е с (3) ( Axв) е* (A4 в) + ЗА 1, 3А е * Yp" у 3 x ЗУ 3 + ЧАзе БА е + ЧBe. yp" З x 32 не ye" - Ур 3х З ЗХ ЗХ Але Ве 37 + ЧBe БАе + ЧАге 3 x = 32 яе 3 x 3х за Зазе 3 x 6te to Be 1 8 А яе 3 x 32 32 е + (6A 4 8 B ) е 3 x 8A Ze comparing both sides & 6A + 3B = 0 8A = 39 24 4 80 = 0-7B --3| | A = -

3x e .: 3p = (41-3)

Given 3 y' - y = 3948 reducing to charemeteristic equation re m²-1 =0 (m+1)(m-1) = 0 maal, 1 y = C, e²+ (go 2 they Y, e" Y2=0 -X y; - et Y = - y, W= e 42 y,' ya re 4 -20 e -1-1 -2 Particullay solution yplx)= -9,12 y, (x ) f(x) dx + yer wly, Y2) ry, x) flolux wly, Y.) 20 $4,64% 8(x) de (32x631) dr Wly,49 -2 بدل -16 x 2x die Swedende suv -fu Judu = au-juder v dy dx CS Scanned with CamScanner

u=x 24 211 Szept des to - dx 221 27 ro els C 니 2 2x 19,6x) for) dv=p2x dic xe 2 Gq (x)f(x) dxeda wly,yo) die wly,y) 2x9 3 (x-13 8634 (x-_) o 'e 3) ( 3276 dic tyl -2 47 =-16 Sacs KP 421 е. xp. = -16 X û ul ЧХ e -16 Corea Send Jo-16) (2-4) (x - 5) 16 9,1») f(x)dxd ५४ -ye - ( دا ، لا أحبا Yp = 80 KE {-4 -40%*(x-1) '(-1)-4032 (x - 5) ( 87-4-4x+1] 034 / 42 - 3 ks 31 We yp are a uns =)Yes the answers CS Scanned with CamScanner