2. (10 points) Consider the initial value problem
$$\frac{dy}{dx} = x^2 + 2y^2, \quad y(1) = 0$$
(a) Using Euler's method with two steps, estimate $y(3)$ by filling in the table below (although you should redraw the table on your own paper and make it larger to show all your work for the values in your table). After filling in the table, make sure you state your estimate of $y(3)$.
n $x_n$ $y_n$ $m = \frac{dy}{dx}$
0 1 0
1
2
(b) Using Euler's method with four steps, estimate $y(3)$. You should create your own table similar to part (a).
