a) By using the Laplace transform, solve the following differential equation y"+y=1-H(t-3m), y(0)=0, y'(0) = 1. b) Using

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A By Using The Laplace Transform Solve The Following Differential Equation Y Y 1 H T 3m Y 0 0 Y 0 1 B Using 1 (21.89 KiB) Viewed 33 times

a) By using the Laplace transform, solve the following differential equation y"+y=1-H(t-3m), y(0)=0, y'(0) = 1. b) Using Laplace transform, solve the system da UTH SUP dt=4 = 1, dy dt +2=e¹-1, UTM UTM given that r(0) = -1 and y(0) = 0. UTM & UTMUTY QUESTION 2 (15 MARKS) periodic function f(r) is defined by f(x)=x² +3 for 2 <I<2 (6 marks) (9 marks) nd f(x) = f(x+4). i) Sketch the graph of the function for -6 <r<6. Then, determine whether f(x) is even, odd or neither. ii) Hence, find its Fourier series. TM &UTMUTM marks) (12 marks)