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4. Solve the following differential equations: d'r + x = 3 sin(2t) given that a = 0 and d=0 when t=0 dt²

4. Solve the following differential equations: d'r + x = 3 sin(2t) given that a = 0 and d=0 when t=0 dt²

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 15CR
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4. Solve the following differential equations: d²x (a) + x = 3 sin(2t) given that x = 0 and d=0 when t = 0 dt² Ans, dy dy (b) -2 + + 7y= 2y given that y = 1 when x = 0 and y = 2e when x = dx dx² 풍 (c) dx +4 dt² dt + 4x = 12e²t given that x = -1 and = 5 when t = 0 (a) x(t) = 2 sin(t) — sin(2t) (b) y(x) = e* (2 sin(2x) + cos(2x)) (c) x(t) = ½ (3e²t - 7e-2t)
Transcribed Image Text:4. Solve the following differential equations: d²x (a) + x = 3 sin(2t) given that x = 0 and d=0 when t = 0 dt² Ans, dy dy (b) -2 + + 7y= 2y given that y = 1 when x = 0 and y = 2e when x = dx dx² 풍 (c) dx +4 dt² dt + 4x = 12e²t given that x = -1 and = 5 when t = 0 (a) x(t) = 2 sin(t) — sin(2t) (b) y(x) = e* (2 sin(2x) + cos(2x)) (c) x(t) = ½ (3e²t - 7e-2t)
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