Consider the Following Initial Value Problem on the Interval [0

Short Answer

Consider the following initial value problem on the interval [0, 1]

Approximate the solution y(t) at t = 2.5 using the fourth-order backward differentiation formula with step size h = 0.05. Using the Runge-Kutta method you are provided with some initial Y_n values to start the fourth-order backward differentiation formula.
Y₁ = 2.157777
Y₂= 2.3322791
Y₃ = 2.5253944
Use the fourth-order backward Euler differentiation formula to compute the following approximation. Express your answer accurate to 6 decimal places.
Y₄ = ________