Assignment 1 Problems

Assignment # 1 (Problems) Ex. 4.1 Find the Laplace transform of 4: ⎧2t + 1 0 ≤ t < 1 f (t ) = ⎨ t >1 ⎩ 0 13: f (t ) = te 4t 25: f (t ) = (t + 1) 3 31: f (t ) = 4t 2 − 5 sin 3t

Ex. 4.2 Find the inverse Laplace transform of 5: L

-1 ⎧ ( s

⎨ ⎩

+ 1)3 ⎫ ⎬ s4 ⎭

8: L

-1 ⎧ 4

6 1 ⎫ ⎨ + 5− ⎬ s + 8⎭ ⎩s s

11: L

-1 ⎧

5 ⎫ ⎨ 2 ⎬ ⎩ s + 49 ⎭

33: Solve the equation

y '+6 y = e 4t , y (0) = 0 Ex. 4.3 Find F (s ) or f (t ) 4: L {t10e −7 t } 7: L {et sin 3t} 15: L

s ⎫ ⎬ ⎨ 2 ⎩ s + 4s + 5 ⎭

-1 ⎧

19: L

-1 ⎧

2s − 1 ⎫ ⎨ 2 3⎬ ⎩ s ( s + 1) ⎭

22: Solve using Laplace transform y '− y = 1 + tet , y (0) = 0 39: Find Laplace or the inverse Laplace transform L {tu (t − 2)} 43: ⎧ e −2 s ⎫ L -1 ⎨ 3 ⎬ ⎩ s ⎭ Ex. 4.4 7: Use theorem 4.8 to find the Laplace transform L {te 2t sin 6t} 21: Use theorem 4.9 to find the Laplace transform L {e − t * et cos t} 25:

{∫ e cosτ dτ } L {∫ τ e dτ }

L 27:

t

−τ

0

t

t −τ

0

32: Use (8) to evaluate the inverse transform ⎧ 1 ⎫ L -1 ⎨ 2 ⎬ ⎩ s ( s − 1) ⎭