PYTHON CODE:

= = 2 2 Consider the ordinary differential equation f'(x) = 4 cos(2x) + x with initial condition 2 X f(0) 0. Use Euler's method (pseudocode provided below) with step size 8 = 0.1 to obtain and plot an approximate solution to the provided ODE over the interval [0, 10). Do not use the append function (slow!). In the same plot, plot the true solution + 4 sin(x) cos(x). . 2 Pseudocode for (simplified) Euler's method: 1: Fix step size 8 and set n = b=a, where a and b are the start and end points respectively of the desired interval to solve over. Set yo = f(0). 2: for i = 1, 2, 3.., n - 1, set yi = yi-1 +8* f'(i.) Yi The "approximate solution is then given by the points (i *d, yi) for i = 0, 1, 2, ...,n-1. = - = > 2 9 9 =