Hi this is from the book Differential Equations With Matlab 3rd edition by Hunt, Lipsman, Osborn, and Rosenberg. Does anyone have experience with matlab and can solve this?

15. This problem is based on Problems 18 and 19 in Boyce & DiPrima, Section 3.8. Consider the initial value problem

u'' + u = 3 cos(t), u(0) = 0, u'(0) = 0.

(a) Find the solution (using dsolve). For = 0.5, 0.6, 0.7, 0.8, 0.9, plot the solution curves on the interval 0 t 15. Note that 0 = 1 is the natural frequency of the homogeneous equation. Describe how the solution curves change as gets closer to 0. (b) Note that the formula you found in part (a) is invalid when = 1. Find and plot the solution curve for = 1 on the interval 0 t 15. Based on the discussion of forced vibrations in your text, what phenomenon should be exhibited for this value of ? Corroborate your answer by plotting on a longer interval. (c) Plot the solution for = 0.9 on a longer interval and compare it with the solution from part (b). What phenomenon is exhibited by the curve for = 0.9?