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  3. 3. solve the following differential equation x^2y�

3. Solve the following differential equation x^2y’’ − 2xy’ + 5y = 0. A coil spring is...

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3. Solve the following differential equation

x^2y’’ − 2xy’ + 5y = 0.

  1. 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)   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

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