Question 4 Consider the system of differential equations After taking the Laplace transform, the system...

 

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Question 4 Consider the system of differential equations • After taking the Laplace transform, the system can be written as [x' (t) = 4x(t)- y(t), Ly' (t) = 2x (t) + y(t) (integer), a2 = • Solve for X = 'with initial conditions (0) = 1, y(0) = -1. (sa₁) X+Y=a₂ a3X + (s-1)Y = 04 (integer), a3 = bi+b₂8 s²-58+b3 and thus determinen b₁ = (integer), b₂ = • Now take the inverse Laplace transform to find x(t) = L¯¹{X(s)} = c₁e³t+c₂est. Thus determine c₁ (integer) and c3 = , where X = L{x(t)} and Y = L{y(t)}. Determine a₁ = (integer) and a4 = (integer). (integer) and b3 (integer). (integer), C₂ = (integer). 10 pts Question 4 Consider the system of differential equations • After taking the Laplace transform, the system can be written as [x' (t) = 4x(t)- y(t), Ly' (t) = 2x (t) + y(t) (integer), a2 = • Solve for X = 'with initial conditions (0) = 1, y(0) = -1. (sa₁) X+Y=a₂ a3X + (s-1)Y = 04 (integer), a3 = bi+b₂8 s²-58+b3 and thus determinen b₁ = (integer), b₂ = • Now take the inverse Laplace transform to find x(t) = L¯¹{X(s)} = c₁e³t+c₂est. Thus determine c₁ (integer) and c3 = , where X = L{x(t)} and Y = L{y(t)}. Determine a₁ = (integer) and a4 = (integer). (integer) and b3 (integer). (integer), C₂ = (integer). 10 pts

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