Determine the inverse Laplace transform of the function below. 4s +37 s² +6s+34 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. L-1 4s +37 $²2+6s+34 Properties of Laplace Transforms L{f+g} = L{f} + L{g} L{cf} = c£{f} for any constant c Leatf(t)} (s) = L{f}(s-a) L {f'} (s) = s£{f}(s) - f(0) L {f'' (s) = s² L{f}(s) - sf(0) - f'(0) L {f(n)} (s) = s£{f}(s)-s-1f(0)-s-2f'(0)-... -f(n-1) (0) dn L {t^f(t)} (s) = (-1)^- dsn = £¯¹ {F₁} + £¯ £¯1{F₁+F2} L1¹{CF} = c£¯¹{F} (L{f}(s)) Table of Laplace Transforms X f(t) 1 eat t", n=1,2,... sin bt cos bt eat,n=1,2,.... eat sin bt eat cos bt F(s) = L{f}(s) 1 s 1 s-a n! Sn+18>0 ,S>0 ,S> 0 b s² + b² ,s > 0 S s²+ b² n! (s-a)n +1 b ,S>0 .s> a (s-a)² + b² s-a (s-a)² + b² .s> a .s> a
Determine the inverse Laplace transform of the function below. 4s +37 s² +6s+34 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. L-1 4s +37 $²2+6s+34 Properties of Laplace Transforms L{f+g} = L{f} + L{g} L{cf} = c£{f} for any constant c Leatf(t)} (s) = L{f}(s-a) L {f'} (s) = s£{f}(s) - f(0) L {f'' (s) = s² L{f}(s) - sf(0) - f'(0) L {f(n)} (s) = s£{f}(s)-s-1f(0)-s-2f'(0)-... -f(n-1) (0) dn L {t^f(t)} (s) = (-1)^- dsn = £¯¹ {F₁} + £¯ £¯1{F₁+F2} L1¹{CF} = c£¯¹{F} (L{f}(s)) Table of Laplace Transforms X f(t) 1 eat t", n=1,2,... sin bt cos bt eat,n=1,2,.... eat sin bt eat cos bt F(s) = L{f}(s) 1 s 1 s-a n! Sn+18>0 ,S>0 ,S> 0 b s² + b² ,s > 0 S s²+ b² n! (s-a)n +1 b ,S>0 .s> a (s-a)² + b² s-a (s-a)² + b² .s> a .s> a
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.1: Inverse Functions
Problem 51E
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