I just want to see if I am approaching problem 3 correctly T

I just want to see if I am approaching problem #3 correctly. The following is the answer I have & the work is also attached:

Problem #3: (1.0, 2.18750)

Problem #1: Find the approximate solution of the following initial value problem at t-1. Use the Euler method with the step size h 0.25 In all your intermediate computations and answer, please keep at least six decimal places. y\' = y2 + 1, y(0)-1 Problem #2: Find the approximate solution of the following initial value problem at t-2. Use the Euler method with the step size h-05. In all your intermediate computations and answer, please keep at east six dec nal places. y dt y(1)-0 =y41+ y, Problem #3: Find the approximate solution of the following initial value problem at t-1. Use the improved Euler method (Heun formula with the step size h = 0.5 In all your intermediate computations and answer, please keep at least six decimal places y\' = 2y-3t, y(0) = 1 Problem #4: Find the approximate solution of the following initial value problem at t Use the Runge-Kutta method with the step size h = 0.5 In all your intermediate computations and answer, please keep at least six decimal places Problem #5: Find the approximate solution of the following initial value problem at t 3 Use the Runge Kutta method with the step size h 0.5. In all your intermediate computations and answer, please keep at least six decimal places. dt = r + 1, = y2 + 1, y(2) = 0 y(2)-

Solution

In my view your answer and approach is correct.

well done.