Let y(x) be the solution of y' = y − 4x such that y(1) = 1. Using a step size of 0.5, set y0 = y(1) = 1 and apply Euler's Method to approximate the values y1, y2, y3, and y4

Use one step of Euler’s method to approximate y(0.1 + π/4 ) if y′ = xsin(x + y) and y( π/4 ) = 0.

Y 11) Given y'= xy² + and y(1) = 1. X a) Use the Euler's and RK4 Methods to find a four decimal approximation of y(1.5) using h = 0.1. b) Find the Exact solution analytically. c) Provide a table of values for all three (Exact, Euler, and RK4) methods leading to y(1.5) and plot them on the same axis, as discussed in class!!

Apply the improved Euler method to approximate the solution on the interval [0, 0.5] with step size h= 0.1. Construct a table showing values of the approximate solution and the actual solution at the points x 0.1, 0.2, 0.3, 0.4, 0.5. y =y-x-3, y(0) = 1; y(x) = 4 +x-3 e* Complete the table below. (Round to four decimal places as needed.) 0.1 0.2 0.3 0.4 0.5 Actual, y (Xn) Improved Euler, yn