Let y = f(x) be the solution to the differential equation 𝑑𝑦𝑑𝑥=𝑓′(𝑥) with initial condition f(2) = 3. Selected values of f' are given in the table above. What is the approximation for f(2.4) if Euler’s method is used, starting at x = 2 with two steps of equal size?

Let 𝑦=𝑓(𝑥) be the solution to the differential equation 𝑑𝑦𝑑𝑥=2𝑥+𝑦 with initial condition 𝑓(1)=0. What is the approximation for 𝑓(2) obtained by using Euler’s method with two steps of equal length, starting at

Use Euler's method with step size 0.1 to estimate y(2.5), where y(x) is the solution of the initial-value problem y' = 3y + 2xy, y(2) = 1. (Round your answer to four decimal places.)

Use Euler's method with step size 0.5 to compute the approximate y-values y1, y2, y3 and y4 of the solution of the initial-value problem y' = y − 5x, y(3) = 0.y1 = y2 = y3 = y4 =

Consider the initial value problemy′(t) = cos(y), y(0) = 0.(i) Apply 4 steps of forward Euler method with the step size h = 12 to approximately findy(2). Show at least 4 decimal places in your calculations. [10 marks](ii) Apply 2 steps of Heun’s method with the step size h = 1 to approximately find y(2).Show at least 4 decimal places in your calculations.

Use Euler's method with step size 0.2 to estimate y(1.4), where y(x) is the solution of the initial-value problem y' = 4x − 3xy, y(1) = 0. (Round your answer to four decimal places.)y(1.4) =