Question

3. Solve the following differential equation

x^2y’’ − 2xy’ + 5y = 0.

4. A coil spring is suspended from the ceiling, a 16-lb weight is attached to the end of it, and the weight then comes to rest in its equilibrium position. The mass is in a medium that exerts a viscous resistance of 8 lb when the mass has a velocity of 1 ft/s. It is then pulled down 12 in. below its equilibrium position and released with an initial velocity of 2 ft/sec, directed upward.

(a)   Use the Laplace transform to determine the resulting displacement of the weight as a function of time; the solution of the initial value problem

                                          1/2y’’ + 8y’ + 50y= 0;        y(0) = 1, y^’(0) = −2.

(b)   Write the solution in the form y(t) = Re^−µt cos(ωt − φ). Please leave the solution in exact form.

Please solve both with steps

Answer 1