QUESTION 1 (15 MARKS) a) Solve the initial value problem using Laplace transform UTM GU UTM UTM MUTM UTM +2y = 26sin 3t,

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Question 1 15 Marks A Solve The Initial Value Problem Using Laplace Transform Utm Gu Utm Utm Mutm Utm 2y 26sin 3t 1 (89.54 KiB) Viewed 22 times

QUESTION 1 (15 MARKS) a) Solve the initial value problem using Laplace transform UTM GU UTM UTM MUTM UTM +2y = 26sin 3t, y(0) = 3. UTM SUT b) Use Laplace transform to solve the system of differential equations UTM UTM UTM UTM (7 marks) +x=y+3e²MUIM UTM MUTM da 二 - x = 4y, dt 5 UTM & UTM dy dt given that at t=0, x= 3, and y = 0. QUESTION 2 (15 MARKS) UTM GUTM A half range periodic function f(x) is defined by f(x)=x-1, 0<x< 1, f(x) = f(x+2). (8 marks) STO i. Sketch the graph of even extensions of f(x) in the interval -4 < x < 4 and find its Fourier series. (8 marks) ii. Sketch the graph of odd extensions of f(r) in the interval -4 < x < 4 and find its Fourier series. (7 marks) BUT 07