Using three terms in the Taylor series given in Eq. (12)

Using three terms in the Taylor series given in Eq. (12) and taking h = 0.1, determine approximate values of the solution of the illustrative example y? = 1 ? t + 4y, y(0) = 1 at t = 0.1 and 0.2. Compare the results with those using the Euler method and with the exact values. Hint: If y? = f(t, y), what is y??? In each of Problems 15 and 16, estimate the local truncation error for the Euler method in terms of the solution y = ?(t). Obtain a bound for en+1 in terms of t and ?(t) that is valid on the interval 0 ? t ? 1. By using a formula for the solution, obtain a more accurate error bound for en+1. For h = 0.1, compute a bound for e1 and compare it with the actual error at t = 0.1. Also compute a bound for the error e4 in the fourth step.