3. Solve the following differential equation
x^2y’’ − 2xy’ + 5y = 0.
- A coil spring is suspended from the ceiling, a 16-lb weight isattached to the end of it, and the weight then comes to rest in itsequilibrium position. The mass is in a medium that exerts a viscousresistance of 8 lb when the mass has a velocity of 1 ft/s. It isthen pulled down 12 in. below its equilibrium position and releasedwith an initial velocity of 2 ft/sec, directed upward.
(a)Â Â Â Use the Laplacetransform to determine the resulting displacement of the weight asa function of time; the solution of the initial value problem
                                         1/2y’’ + 8y’ + 50y=0;        y(0) =1, y’(0) = −2.
(b)   Write thesolution in the form y(t) =Re−µt cos(ωt − φ).Please leave the solution in exact form.
Please solve both with steps
