Question

B1: (24 marks) Solve the following initial value problems. When it is possible, express the solutions explicitly in terms of the independent variable. a) (t? + 1) 44 +3ty = 6t, y(0) = -1 b) * = y(1 – y), y(0) = 1/2 c) dy + +y = ty?, y(1) = 1 - 4y = 3e2t, y(0) = -2, y'(0) = 0

Answer 1

dy solve the following initial value problem when it is possible express the solution explicitly in terms of the independent variable (9). (6+1) dy + 364 64 9101- - P (H)= 3 dyt 3+ y = b (+²+1) (+²+1 1 SLH = 6t ft), tt Tea Sedie Sonne If= e = e = 21 094821) ē iselt 0 IF (tywatory general solution of up Mow is 3 Love » de to - 8. Av Jenten, to over het go. As to getum c. comme dt to - TT Scanned with CamScanner 2 x 3/2

Y(+1) - 2014 ar .: 71011 dy = 401-4) - y101 = (12) y dt ay = dt yli-Y) dy I dy (1-7) = at Integrating lny loll-y) = 1 + anc -47 } + Inc - L E mm. CS Scanned with Hol = 1 CamScanner

1-NE ㅋ Now ( 1 requried son 19 = 알 특 뿌는g ty SN) -1 | + et - ① put + = u ㅗ 화 따 = 이쁘 따 pulting in o 9 -Lx = -t ① 아 CS stered withpl H = -46, SCH=-t CamScanner

1 Spar lidt -ent IF = e se se Elle Now general son of cas ist 44= S-t. I do te -156 = 1² + ct y (1 = 1 1 E-1 tc → C = -2 - 30 <- -'-24 dy -44 = 3et, 41013 -2, 510150. How quriliardy equation <? 4 =0 = ca 12 Mow cs Scanned with uét 522* S

3 en PT = foi f(2)=0 so PLC Fires PI = great 2x2 Denise PI = Mow general solution y: CE + PI (y= u 2 + ca e y'a 2444=25€ + Vetutes Ics Scanned with CamScanner

go1 = -2 from (s 3 2= 4+ cq – 0 y'colo de os 14-29 + 2 O 244- - A. from (1) 815) 4- 32 - ноо ача) 5. Ih is о yz Z - lah 19 16 Scanned with CamScanner