9. Do Prob. 7 using Euler's method with h = 0. 1 and colli- 1-4 EULER METHOD Do 10 steps. Solve exactly. Compute the error. Show pare the accuracy. details. 10. Do Prob. 7 using the improved Euler method, 20 steps 1. y' + 0.2y = 0, y(0) = 5, h = 0.2 with h = 0.05. Compare. 2. y' = TV1 -y2, >(0) = 0, h =0.1 11-17 CLASSICAL RUNGE-KUTTA METHOD 3. y' = (y - x)2, W0) = 0, h = 0.1 OF FOURTH ORDER 4. y' = () + x)2, >(0) = 0, h =0.1 Do 10 steps. Compare as indicated. Show details. 11. y' - xy= = 0, y(0) = 1, h = 0.1. Compare with 5-10 IMPROVED EULER METHOD Prob. 7. Apply the error estimate (10) to y10- Do 10 steps. Solve exactly. Compute the error. Show 12. y' = y - y , >(0) = 0.2, h = 0.1. Compare with details. Prob. 8. 5. y' = y, y(0) = 1, h = 0.1 13. y' = 1 + yz, y(0) = 0, h = 0.1 6. y' = 2(1 + y2), >(0) =0, h = 0.05 14. y' = (1 - x-])y, y(1) = 1, h = 0.1 7. y' - xy2 = 0, W0) = 1, h=0.1 15. y' + y tan x = sin 2x, y(0) = 1, h = 0.1 8. Logistic population model. y' = y - y . y(0) = 0.2, h = 0.1 16. Do Prob. 15 with h = 0.2, 5 steps, and compare the errors with those in Prob. 15