SharmaMAT275ONLINEBFall2015 Problem 1. 1.(5 pts) Write the given second order equation as its equivalent system of first order equations. u−3u−3.5u=5sin(3t),u(1) =3,u(1) =4.5 Usevto represent the ”velocity function”, i.e.v=u(t). Usevandufor the two functions, rather thanu(t)andv(t). (The latter confuses webwork. Functions like sin(t)are ok.) u= v= Now write the system using matrices: d dt uv=u v + and the initial value for the vector valued function is: u(1) v(1) =. -2*eˆ(-9*t)*1 + -1*1 Problem 3. 3. (5 pts) Solve the system dx dt = 3 9 − 1 − 3 x with x ( 0 ) = 2 4 . Give your solution in real form. x 1 = , x 2 = . Answer(s) submitted: •3.5•-2*eˆ(-9*t)*4 + -1*1 •-2*eˆ(-9*t)*1 + -1*1 Problem 3. 3.(5 pts) Solve the system dx dt =39 −1−3 x withx(0) =2 4 . Give your solution in real form. x1 =, x2 =. Answer(s) submitted: •2+42t •4-14t (correct)