Question

Use the method of variation of parameters to find a particular solution of the following differential equation. y" - by' +9y = 2e 3x What is the Wronskian of the independent solutions to the homogeneous equation? W(11.72) = 0 The particular solution is yp(x) =

Answer 1

30 4"-6y'+90 - piesa noua au villany equation suc h en m?: 6m +9 30. (m-3) (m-3 2-0.. m = 3,3 complementary Solution is cf = (ento x) e acie tone and het y = 0 & Je = x x be two wineasley independent solutions of Corros ponding homogeneous equation ? 139 two 090 20

to (4 ч.) - 9. : " 32 г мез" - зах - я кзе*, * 3 g - x3e + е за со (915) - Ге" 37 320 . xe te 2 - e г 39 No ( 7 2 4c2 3x 3 x 38 - 3 37 3 е ,е 37 31 е . е 3 - 9 + от e x ст w (82, ч.) - е The partcular solution Чp(+) = 49, +v, 2(x) = 2 е u - - [ 5, 7 см ) ди w (Я. •42) - че": "h - (* * * - - 2 х = - 22

V: [Ч, СУ) dч - РеЎ? » (Я •42) х = . Г р() - ау, 1 ч 2 та — — ве 3 + Х аў у е = x e – m° 3 Уptx) = x'e3x — : 6 90 Thu x w(), 3. ) = ex - Яр Ся) = ne 3х.