Consider the initial value problem on the interval [0, 1]. y' = 4y - X (0) = -1 (0.1) = (a) Use Euler's method with step size h = 0.1 to approximate points along the solution curve of the initial value problem over the given interval. (Round your answers to four decimal places.) (0.2) = -0.2 (0.3) = (0.4) = (0.5) = (0.6) = y(0.7) = (0.8) = (0.9) = (1) = (b) Find an analytical solution. y(x) = (c) Plot the solution curve along with the approximate points. 0.6 0.8 70 1,0 U.Z +04 0.6 0.8 1.0 -10 -10 60 -20 -20 501 50 -30 -30 -40 -40 30- -50 -50 20 20- -60 -60 O-70 L O-70 O 0.2 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.8 - X 1.0 Additional Materials Tutorial11. [0/5.55 Points] DETAILS PREVIOUS ANSWERS ZILLDIFFEQ9 9.1.001. Use the improved Euler's method to obtain a four-decimal approximation of the indicated value. First use h = 0.1 and then use h = 0.05. y' = 3x - 4y + 2, y(1) = 3; y(1.5) h = 0.1 y(1.5) # 1.1494 X h = 0.05 y(1.5) ~ 1.2409 X Need Help? Read It Watch It 12. [-/5.55 Points] DETAILS ZILLDIFFEQ9 9.1.002. Use the improved Euler's method to obtain a four-decimal approximation of the indicated value. First use h = 0.1 and then use h = 0.05. y' = 6x - By, y(0) = 2; y(0.5) y(0.5) ~ (h = 0.1) y(0.5) (h = 0.05) Need Help? Read It Submit Answer 13. [-/5.55 Points] DETAILS ZILLDIFFEQ9 9.1.003. Use the improved Euler's method to obtain a four-decimal approximation of the indicated value. First use h = 0.1 and then use h = 0.05. y' = 1 + yz, y(0) = 0; y(0.5) h = 0.1 y(0.5) ~ h = 0.05 y(0.5) Need Help? Read It