An improved method that is similar to Euler's method is what is usually called the Improved Euler's method. It works like this: Consider an equation y = f(z,y). From (m, n), our approximation to the solution of the differential equation at the n-th stage, we find the next stage by computing the a-step In+1 = 2n + h, and then ki, the slope at (zn. y). The predicted new value of the solution is 2n+1 =yn+h+k. Then we find the slope at the predicted new point k= f(n+1+1) and get the corrected point by averaging slopes Suppose that we use the Improved Euler's method to approximate the solution to the differential equation dy y(0.3) = 1. dz 71 We let zo 0.3 and yo = 1 and pick a step size h = 0.25. Complete the following table: 0 1 2 In 0.3 h Yn+1=Yn +(K+k). Y 1 = x -0.5y, 1. 1. k -0.2 1. Cookies help us deliver our services. By using our services, you agree to our use of cookies. ON Fn+1 0.95 Learn more 1. k 0.075 n 0 12 3 4 In 0.3 12 1. 3/m 1 1. 2 ky y(x)= Thus the actual value of the function at the point r= 1.3 is y(1.3)= help (numbers) While the approximate solution found above is y(1.3) -0.2 1. 4. An+1 0.95 help (numbers) The exact solution can also be found for the linear equation. Write the answer as a function of a. help (formulas) help (numbers) 1. k 0.075 I am finishe 4. 1.