5. 10 points) (MATLAB) Numerical solutions of dynamical systems. In this exercise, you are asked to use the MATLAB function ode45 to compute numerical solutions of dynamical systems in state space. For each dynamical system below, you need to plot a (numerical) solution to the initial value problem on the given time interval. If the dimension of the system is greater than 1, you need to plot each component of the solution. If you have not used ode45 in MATLAB before, you should read its documentation and understand the examples therein before working on these problems. The documentation can be accessed by running 'doc ode45' in the command window. You may also want to learn about function handles (represented by the operator Q), which can be viewed as the MATLAB equivalent of "pointers" for people familiar with C/C++ (a) Inverted pendulum without erternal torque. In class, we showed that by choosing the state variables 1 = and z2 = , where is the angular position of the pendulum, the system can be written as mgl sin -bx2