Answer Happy

I need help solving these 3 using improved Euler Method and solve explicitly
Famous Numbers Revisited The following problems describe the numbers e≈ 2.7182818, In 2≈ 0.6931472, and ≈ 3.1415927 as specific values of certain initial value problems. In each case, 10, 20, 40, ... subintervals (doubling n apply the improved Euler method with n = each time). How many subintervals are needed to obtain-twice in succession-the correct value of the target number rounded to five decimal places? 1. The number e = y(1), where y(x) is the solution of the initial value problem dy/dx = y, y(0) = 1. 2. The number In 2 = y(2), where y(x) is the solution of the initial value problem dy/dx = 1/x, y(1) = 0. 3. The number = y (1), where y(x) is the solution of the initial value problem dy/dx = 4/(1+x²), y(0) = 0.