Please include matlab code. Let me know if additional information is needed. Thank you.

A solution of a second order linear differential equation is called oscillatory if it changes sign infinitely many times and nonoscillatory if it changes sign only finitely many times. In this problem, we will be interested in determining the oscillatory nature of nonzero solutions to some second order linear ODEs. First consider the equation y" + ky = 0, where k is a constant. If k > 0, it has the general solution y = R cos (Squareroot k x - delta), with R greaterthanorequalto 0, delta arbitrary. The constant R is called the amplitude, and d is called the phase shift. From this formula we see that every solution y(x) has infinitely many zeros, and hence changes sign infinitely many times, i.e., is oscillatory. If k 0? How many zeros could a solution have on the positive x-axis? Do the graphs you plotted in part (a) agree with these results