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-4, y(0) = 3; y(x) = 5+x-2ex ... Complete the table below. (Round to four decimal places as needed.) Xn 0.1 0.2 0.3 33 Actual, y (xn) 0.4 0.5

sketch an approximate solution curve that passes through each of the indicated points. Use different colored pencils for each solution curve.

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-2x-4, y(0) = 3; y(x) = 6+2x-3ex Complete the table below. (Round to four decimal places as needed.) Xn Actual, y (xn) 0.1 0.2 0.3 0.4 0.5

Find General Solution of y" + y" = 0.

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-3x-2, y(0) = 4; y(x) = 5 + 3x - ex Complete the table below. (Round to four decimal places as needed.) Xn Actual, y (Xn) Improved Euler, yn 0.1 0.2 0.3 0.4 0.5

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-3x - 3, y(0) = 4; y(x) = 6 + 3x - 2ex Complete the table below. (Round to four decimal places as needed.) Xn Actual, y (Xn) Improved Euler, yn 0.1 0.2 0.3 0.4 0.5

Solve for For b = 5 and  c =3

Determine the value of k that will make y = 2cos(2x) a solution to ky - y" = y. Ok = 5 Ok=0 Ok = -3 Ok=-6

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' = -3y, y(0) = 3; y(x) = 3e-3x Complete the table below. (Round to four decimal places as needed.) Xn Actual, y (xn) 0.1 0.2 ☐ 0.3 ☐ 0.4 ■ 0.5 10

Provide the necessary solution: