Question: a) Solve the following ODE. y+y = 1, y(0) = 0, y'(0) = 1 b) Solve the following initial value problem using Laplace transform

a) Solve the following ODE. y"+y = 1, y(0) = 0, y'(0)

a) Solve the following ODE. y"+y = 1, y(0) = 0, y'(0) = 1 b) Solve the following initial value problem using Laplace transform method. y" - 4y' + 13y = 8(t-3), y(0) = 0, y'(0) = 3 [10 Marks] c) Solve the following system of ODEs by let x(t) and y(t) be the two functions of the variable t. dx dt dy dt 2x - 3y =y-2x [5 Marks] x(0) = 1, y(0) = 2 [10 Marks]

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