Homework 5 is to solve three ordinary differential equations. For each equation, solve it for the range 0-7, with 700 data points. Use the python function odeint! (For reference, see verysimpleODE.py and some of the other examples.)
You will turn in a single python file called hw5.py which solves the three problems. For each problem graph the requested items. Note that y' is the first derivative of y with respect to t. Likewise, y" is the second derivative of y with respect to t. Note that np.cos() and np.sin() are computing values in radians.
Problem 1: y’ = cos2(t); initial value: y(0)=1. Plot y vs t.
Problem 2: y’ = 2y + 2e3t; initial value y(0) = 5. Plot y vs t.
Problem 3: y” = -2y + 2y'; initial values y(0) = 1, y’(0) = 1. Plot y vs t and y’ vs t on the same plot.
