Chapter 5.2, Problem 5E

Approximate the solution to IVP:y' = 1 + (t − y)^2  , 2 ≤ t ≤ 3,  y(2) = 1at t = 2.5 using h = 0.5, and1. Euler’s method,2. Taylor method of order 2,3. Runge-Kutta method of order 2,4. Runge-Kutta method of order 4,

find the Taylor polynomial at x = a for the given function. f (x) = x ln(x), T4, a = 1

Find the Laplace transformY(s) = L{y} of the solution of the given initial value problem.