Question: Question 4 (30 marks) (a) Given that x(0) =0, y(0) =a, solve the system of differential equations: dx =x+2y+12e dy -= 4x+3y+18e di (b) Find

Question 4 (30 marks) (a) Given that x(0) =0, y(0) =a,

Question 4 (30 marks) (a) Given that x(0) =0, y(0) =a, solve the system of differential equations: dx =x+2y+12e" dy -= 4x+3y+18e" di (b) Find the general solution for dx -= x +2x, -3x3 dt dx, -=-5x +X, -4X3 di dx -2x, +4x3 dt (c) Use Laplace Transform to solve the differential equation: y'+4y'+ 5y =10e' , y(0) =1, y' (0) =2

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