(b) Consider the following system of coupled differential equations: (t) + x(t)+(t)=1 and +y(t) + y(t)=0,...

 

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(b) Consider the following system of coupled differential equations: (t) + x(t)+(t)=1 and +y(t) + y(t)=0, with initial conditions (0) = 0 and y(0) = 0. Take the Laplace transform of both of these with respect to t to find two simultaneous equations for the Laplace transforms of x(t) and y(t), X(s) and Y(s) respectively. Solve these to show that X(s) [3] 4(s+1) s(3s+2)(x+2) 2 and Y(s) [2] (3s+2)(x+2) (b) Consider the following system of coupled differential equations: (t) + x(t)+(t)=1 and +y(t) + y(t)=0, with initial conditions (0) = 0 and y(0) = 0. Take the Laplace transform of both of these with respect to t to find two simultaneous equations for the Laplace transforms of x(t) and y(t), X(s) and Y(s) respectively. Solve these to show that X(s) [3] 4(s+1) s(3s+2)(x+2) 2 and Y(s) [2] (3s+2)(x+2)