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The differential equation a': + 9 :1: = (1) dt2 describes the motion of a spring subject to a linear restoring force. The characteristic equation is l was in E . which has solution set ' {3'I,3'I} ' n B (see note}. So the solutions to (1) are 83\"., 83\". and any linear combination of them. Note: Use the variable I: in the characteristic equation and use :5 to denote multiplication. For example, if your answer is the equation 21:2 10k + 8 = 0, you would enter 2*k"210*k+8 = 0. To enter a set in Maple, use the curly brackets. For example if your answer is {0, 1} you would enter {0 , 1}. Remember to input the number 1' as a capital I . Since 31% 3tz - cos(3t) = i and _2 - smt3t) = in n we see that cos(3t) and sin{3t) are also solutions. And since - eg = cos(3t} + siu(3t) and . e3ti = ||n 3ft" 3 - we see that any linear combination of e and B Is also a linear combination of cos(3t) and sin(3t) (possibly with complex coefcients). Hence the general solution to (1) is :1: = Acos(3t) + Bl sin(3*t} |n