8 UTM 8 QUESTION 1 (15 MARKS) TM UTM UTM & UTM UTM UTM & UTM 8 UTM & UTM & UTM a) By using the Laplace transform, solve

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8 Utm 8 Question 1 15 Marks Tm Utm Utm Utm Utm Utm Utm 8 Utm Utm Utm A By Using The Laplace Transform Solve 1 (65.9 KiB) Viewed 32 times

8 UTM 8 QUESTION 1 (15 MARKS) TM UTM UTM & UTM UTM UTM & UTM 8 UTM & UTM & UTM a) By using the Laplace transform, solve the following differential equation 6 UTM 8 UTM 25 UTM (0) = 1. b) Using Laplace to solve the & UTM UTM UTM & UTM UTM UTM & UTS UTM UTM y"+y=1-H(t-3m), y(0)=0, UTM 8 UTM dy UTM & UTM & di dt given that x(0)=-1 and y(0) = 0. UTM & UTM BUT QUESTION 2 (15 MARKS) A periodic function f(x) is defined by JTM aut UTM & UTM UTM and f(x) = f(x+4). & UTM y=1, +z=e²-1₁ TUTM UTM UTM UTM & UTM f(x)=x² +3 for 2 < x < 2 & UTM (6 marks) BUTM UTM & UTM AUTM UTM BUTM UTMUT 8 UTM SUT (9 marks) UTM & UT AUTMUT i) Sketch the graph of the function for -6 < a < 6. Then, determine whether f(x) is even, odd or neither. UTM TM ii) Hence, find its Fourier series. (3 marks) WITH (12 marks) UTM SUT AUT