Given f ( x ) = x is a nonzero solution to , obtain a second, linearly independent solution by reduction of order. (b) Use the Wronskian to prove the two solutions are linearly independent. ______________________________________________________________________ 9. (10 pts.) An 8-lb weight is attached to the lower end of a coil spring suspended from the ceiling and comes to rest in its equilibrium position, thereby stretching the spring 0.4 ft. The weight is then pulled down 6 inches below its equilibrium position and released at t = 0. The resistance of the medium in pounds is numerically equal to 2x ′ , where x ′ is the instantaneous velocity in feet per second. (a) Set up the differential equation for the motion and list the initial conditions. (b) Solve the initial-value problem set up in part (a) to determine the displacement of the weight as a function of time. ___________________________________________________________________________ Bonkers 10 Point Bonus: Obtain a condition that implies that will be an integrating factor of the differential equation and show how to compute μ when that sufficient condition is true. Say where your work is for it won’t fit here.
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