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Mat565 Test 2

1) Find the inverse Laplace transform of (s+2)^2/(s-2) using the convolution theorem. 2) Use properties of the inverse Laplace transform to find: a) L^-1{ln((s^2+4)/(s^2+9))} b) L^-1{e^-2s(2s+5)/(s^2+4s+3)} 3) Solve the system of differential equations dx/dt + x + dy/dt + 3y = 2 and dx/dt - x + dy/dt + y = t with initial conditions x(0) = 1 and y(0) = 0.

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257 views6 pages

Mat565 Test 2

1) Find the inverse Laplace transform of (s+2)^2/(s-2) using the convolution theorem. 2) Use properties of the inverse Laplace transform to find: a) L^-1{ln((s^2+4)/(s^2+9))} b) L^-1{e^-2s(2s+5)/(s^2+4s+3)} 3) Solve the system of differential equations dx/dt + x + dy/dt + 3y = 2 and dx/dt - x + dy/dt + y = t with initial conditions x(0) = 1 and y(0) = 0.

Uploaded by

Muhammad Rasydan
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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ASSESSMENT 2

MAT 565
JUNE 2021
PLEASE ANSWER ALL QUESTIONS.
Part A
2
1. Find ℒ −1 {(𝑠+2)2 } by using convolution theorem. (8 marks)
(𝑠−2)

Part B

1. Use appropriate properties of inverse Laplace transform to find

−1 1 𝑠2 +4
a. ℒ { ln⁡ ((𝑠2 2 )} (6 marks)
2 +9)

𝑒 −2𝑠 (2𝑠+5)
b. ℒ −1 { } (5 marks)
𝑠2 +4𝑠+3

2. Solve for 𝒙(𝒕) for a system of linear ordinary differential equations


𝑑𝑥 𝑑𝑦
+𝑥+ + 3𝑦 = 2
𝑑𝑡 𝑑𝑡
𝑑𝑥 𝑑𝑦
−𝑥+ +𝑦 =𝑡
𝑑𝑡 𝑑𝑡
with initial conditions 𝑥 (0) = 1⁡𝑎𝑛𝑑⁡𝑦(0) = 0.
(11 marks)

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