Modify lab04ex2.m so that it solves (l4.7) using euler’s method with n = 1000 in the interval 0 ≤ t ≤ 50 (use the file euler. m from lab 3 to implement euler’s method; do not delete the lines that implement ode45). let [te, ye] be the output of euler, and note that ye is a matrix with two columns from which the euler’s approximation to y(t) must be extracted. plot the approximation to the solution y(t) computed by ode45 (in black) and the approximation computed by euler (in red) in the same window (you do not need to plot v(t) nor the phase plot). are the solutions identical? comment. what happens if we increase the value of n?

Based on the situation in part a, the width of a rectangular garden is x feet, and its length is 5 feet more than twice its width. the right side of the equation, g(x) = 2x2 − 13x + 6, can be factored to g(x) = (2x − 1)(x − 6). this function could represent an inner region of the garden from the first equation, such as a vegetable garden with a border around it. the length of this inner garden would be 2x − 1 feet, and the width would be x − 6, which would leave a 3-foot border around the garden. part d what is the value of g(8) for the function g(x) in part c? what does this value mean in the context of the situation you described in part c?