Question

Determine the form of a particular solution for the differential equation. Do not solve. y"-y=4e2 +772e2 The form of a particular solution is yp(t) = 0 (Do not use d, D, e, E, I, or I as arbitrary constants since these letters already have defined meanings.)

Answer 1

24 7 solution - Given, y - y = 4 + +7+2 Pareti find. Particular solution Upct) of D. EQ, (not Complete solution of o) The particular solution Up (t) of is find by- 8pct) = (D²-DJ 22t =41 et since at at •fal - flaj where, f(a) to. (0) 1 lt² fo (fotol) = 4 et +7 et (2²-2) | CD +2 -(Draj} 2* S 11 24 4 e + 7 2 B +QD+Q-D-2 1 2t 24 +7 } t 2 D +30+2 2* at - 2 é +7 é bd at gt = 2 é t7e Ar Petit (19)} * Te pot 297] (829)+(203. 2 Ypht) = at - 2e t

* 21 43 11g [ (42) () + - 0 ] itp 8 [ http) (bitcotte) 역 니 았t ) 246 + o+t982 니 2 24 e -(1+3) + 4 오 This is particular folution t =ge + gt zge t =ge + e gt e =호 21차 gt [ 2 + - 49 4 2. 2 2 24 e 가치 t