Using Laplace transform methods, solve for t ≥ 0 the following simultaneous differential equations subject to the given initial conditions:

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(a) 2 dx dr (b) (c) 2dx + 4y + 4x-37y=0 2- dr dt d.x dr subject to x = 0 and y = at t = 0 dy + 2 + x - y = 5 sinf dt d.x - 2- dy 2- - 9y=e-2 dr 3dy dr dt subject to x = 0 and y= 0 at t = 0 d.x dt +3 + dy dt +x - y =e' + 2x + y = e- dy dr subject to x = -1 and y = 4 at t = 0 + 5x + 3y = 5e-