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

(a) Given that x(0) =0, y(0) = a, solve the system

(a) Given that x(0) =0, y(0) = a, solve the system of differential equations: dx = x+2y+12e" dt dy = 4x+3y+18e" dt (b) Find the general solution for dx1 = x, + 2x, -3x, dt dx2 =-5x, +X2-4x3 dt -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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