Using Laplace transform methods, solve for t 0 the following differential equations, subject to the specified

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Using Laplace transform methods, solve for t ≥ 0 the following differential equations, subject to the specified initial conditions.

(a) (c) d.x + 3x = e2 subject to x = 2 at t = 0 dt (b) 3- d.x (e) dt dx dr - 4x = sin 2r subject to x = at t

(f) (h) (j) -2/ dx dx +4. + 5x = 3e-1 dr dt subject to x = 4 and dx dx + dr dr subject to x = 1 and dy dy +2-

dx (k) + 8- + 16x = 16 sin 4t dr d.x di subject to x = -and dy dr (1) gdy dt +12- dx dt + 4y = e subject to y

(m) (n) dx dr dx 2- dr d.x dt subject to x = 0, d.x dr dx dx d.x + + dr dr dr + 2x = 2 + 1 subject to x = 0,

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