2. Consider the following initial value problem dy dx = 1+ y², y(0) = 0. = (4) Solve this problem in closed form. Then solve this problem numerically over the interval 0 ≤ x ≤ 0.5 using Euler's method with step size h = 0.1. Present your results in a table, listing, in columns, the values of the mesh points xk, the numerical estimates uk, the exact values yk y(xk) and errors Ck = Uk − Yk. The entries of the latter three columns should be presented to at least five decimal points. - In the problems below: • "DE" denotes "differential equation" "d.e." denotes “difference equation."