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A mass of 1 slug is attached to a spring whose constant is 5 lb/ft. Initially the mass is released 1 foot below the  equilibrium position with a downward velocity of 5 ft/s, and the subsequent motion takes place in a medium that offers a damping force numerically equal to two times the instanta­neous velocity.

(a) Find the equation of motion if the mass is driven by an

external force equal to/(t) = 12 cos 2t + 3 sin 2t.

(b) Graph the transient and steady-state solutions on the same

coordinate axes.

(c) Graph the equation of motion.

solve the given differential equation by undetermined coefficients

y” – 4y = (x2 – 3) sin 2x

y”” – y” = 4x + 2xe-x

solve each differential equation by variation of parameters.

y”+y=tan x

y” -y = sinh2x

solve the given initial-value problem. Use a graphing utility to graph the solution curve.

x2y” – 3xy’ + 4y = 0, y(l) = S, y'(l) = 3

Use the information given in the FIGURE to construct a mathematical model for the number of pounds of salt x1 (t), x2(t), and x3(t) at time t in tanks A, B, and C, respectively.

I’VE ATTACHED THE FIGURE.

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