Question

differential equations

Problem 2 Solve y"+y= ſt/2, if 0 <t<6, if t > 6 y(0) = 6, 7(0) = 8

Answer 1

ost €6 y" ty=/th/2 3 t76 Y() = 6, y'(o)=8 = Laplace transform 7 Taking L{"}+2{y} = { fle} f 147 977 šo 4/2 where E7,6 3 L{y} = 5²kys - Sy()- 4(0) -st fet) de {ooth? e dt. 6 -st s t att e fsesta 2 6 D -St e 2 -St e 3 f 구 -st to e -s $ 2 2 S -65 -65 -6$ be T + e ela - -6S -65 3 e -65 L 3e де + L 2 S2 S u s2 59 L = 2 S2 252T -6S e L +2252 = {alet 8-59-{altes : 252

E6s ) (st) LA = 6St8 + ㅗ S 25 2 2s2 6S 8 이 1 + C + HeS 5줘 252(56) ers 2 6S 2 2계 ( ) + + ㄱ + 51 s E6 ㄴ 글 T S2 번S 6s 8 1) + + / 주두부 두 ㅜ 1번S 2 十] s2 2 15S T S92 e ē8s ㅗ 2. s2 S뤄 s 149=6d 옳 + 8 ㅗ + 뤄 st 회 ~~ éss 65 L S줘 사는 그 5 뤠 sent = 6.Cok +8 St + k -호.(4-60 ut이 t늘 S1이에 6 야 + 캐 10 is Sent + 1 t + 2 보 늘 Sen(16) U11-6) - tutt) 2