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In Problems 18, find the general solution of the given differential equation. In Problems 916, find the particular solution of the initial value problem. In Problems 1720, solve the initial value problem and find the amplitude, frequency, and phase shift of the solution. 21 A massspring system mx" + bx' + kx = 0 has spring constant k = 29, damping constant b = 4, and mass m = 1. At time t = 0, the position is x(0) = 2 and the velocity is x'(0) = 1. Find the position x(t) as a function of time. 22 A massspring system mx" + bx' + kx = 0 has spring constant k = 24, damping constant b = 12, and mass m = 3. At time t = 0, the position is x(0) = 0 and the velocity is x'(0) = 1. Find the position x(t) as a function of time. 23 Show that if y(t) is a solution of a differential equation ay" + by' + cy = 0, such that y(t_{0}) = 0 and y'(t_{0}) = 0 at some time t_{0}, then y(t) = 0 for all t. 24 In the differential equation ay" + by' + cy = 0, suppose that a is positive and c is negative. Show that the characteristic equation has one positive real root and one negative real root, so that the general solution has the form y = Ae^{rt} + Be^{st} where r is positive and s is negative. 25 In the differential equation ay" + by' + cy  0, suppose that a and c are positive and b is negative. Show that there are three cases for the general solution, depending on the sign of the discriminant d:


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