Question 1 (32 marks) (a) (b) Use the Laplace transform to solve the following initial value problem: y"-10y +9y = 5t, y

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Question 1 32 Marks A B Use The Laplace Transform To Solve The Following Initial Value Problem Y 10y 9y 5t Y 1 (340.29 KiB) Viewed 34 times

Question 1 (32 marks) (a) (b) Use the Laplace transform to solve the following initial value problem: y"-10y +9y = 5t, y(0) = -1, y'(0) = 2. [8 marks] Solve the following initial value problem using a Laplace transform method. y" - 6y + 5y = 3e²t, y(0) = 2,y' (0) = 3. [12 marks] Use the Laplace transform to solve the given system of differential equations: dx dy 2-+ dt dt || - 5e dy dx 3 = 5 dt dt Given that when t=0, x= 0 and y = 0. [12 marks]