Question

9. Take the Laplace transform of both sides of the equation below and then solve for Y(s) = L{y}. Do NOT try to find y(t)! y" – 5y' – 36y = sin(3t), y(0) = 5, y'0) = 7

Answer 1

Ques: y"-by' + 3by gen. sin(at) .-- 4-5 & 7)-7 solution: Taking haplace transforms on both sides, we L {y" - sy' + 3 by} = L { sinst} > {{y } - 5 L{2} + 36 L {y} = { sinze} L {y}=Y (8) L {y} = SY(8) -y (0) and, L { y" } = 8² Y(&)- 34(0)-Y'(o). HT Define Then,

L {y}= Y(e? {{y?= 8 Y(3) - 5 L {y" } = 8² Y(*) – 55-7 Putting these equations in , we ger Y(6)– 52-1)-5181 Y(s) — 5) +36.Y(8) Y(8) = 3 → 8² +36).Y(8) – 55-7+25 = 3 82+7 (8=58+ $²49 7 p2_58+36) 4(0)= (58-18) + 3 2 A +9 1 Y(8) - 3 + 58-18 82_58 +36 (2+1)(6=51+36) 458 - 159 → Y(8)= 583–1882 + (8°+9) (055+36)