Let Solve the differential equation using Laplace transforms. y(t) = g(t) = { t if t≤2π 2π if t>2π y" + 16y= g(t), y(0) = 5, y(0) = 5 ift ≤2x ift > 2π function f(t) 1 tn eat sin at cos at sinh at cosh at e-at f(t) U(ta) or Ua(t) (a ≥ 0) (ta) (a> 0) U(t − a)f(t − a) or Ua(t)f(t − a) f(n)(t) (−t)" f (t) - (fg)(t) = f(r)g(t − T) dr Laplace transform F(s) 1/s (s > 0) n!/sn+1 (s > 0) 1/(s – a) (s> a) a/(s²+a²) (s > 0) s/(s² + a²) (s > 0) a/(s² - a²) (s> |a|) s/(s² – a²) F(s+a (s>|a|) -as e S S 0) as e as e S F(s F(n)(s) F(s)G(s) sn ¯¹ƒ (0) — sn−² ƒ'(0) … … … — ƒ (n−¹) (0)
Let Solve the differential equation using Laplace transforms. y(t) = g(t) = { t if t≤2π 2π if t>2π y" + 16y= g(t), y(0) = 5, y(0) = 5 ift ≤2x ift > 2π function f(t) 1 tn eat sin at cos at sinh at cosh at e-at f(t) U(ta) or Ua(t) (a ≥ 0) (ta) (a> 0) U(t − a)f(t − a) or Ua(t)f(t − a) f(n)(t) (−t)" f (t) - (fg)(t) = f(r)g(t − T) dr Laplace transform F(s) 1/s (s > 0) n!/sn+1 (s > 0) 1/(s – a) (s> a) a/(s²+a²) (s > 0) s/(s² + a²) (s > 0) a/(s² - a²) (s> |a|) s/(s² – a²) F(s+a (s>|a|) -as e S S 0) as e as e S F(s F(n)(s) F(s)G(s) sn ¯¹ƒ (0) — sn−² ƒ'(0) … … … — ƒ (n−¹) (0)
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
Section11.1: Solutions Of Elementary And Separable Differential Equations
Problem 54E: Plant Growth Researchers have found that the probability P that a plant will grow to radius R can be...
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