Use the improved Euler method with a computer system to find the desired solution value. Start with step size h = 0.1,and then successively smaller step sizes until successive approximate solutions at x = 2 agree rounded off to fourdecimal places.y' = x² +9y² - 7₁ y(0) = 0, y(2) = ?The approximate solution at x = 2 is y(2)=|||.

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Answered: Use the improved Euler method with a…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Given y' = y cost, 0sts 1, y(0) = 1 and N= 5. Then using Euler's method, the approximation of the solution at t=0.4 ( use 4 digit rounding) Select one: a. 1.2216 b. 1.4352 c. 1.4399 d. 1.2145
Use Euler's method to approximate y(1.8). Start with step size h=0.1, and then use successively smaller step sizes (h=0.01, 0.001, 0.0001, etc.) until successive approximate solution values at x = 1.8 agree rounded off to two decimal places. y'=x² + y²-2. y(0) = 0 The approximate solution values at x = 1.8 begin to agree rounded off to two decimal places between (Type an integer or decimal rounded to two decimal places as needed.) ▾ So, a good approximation of y(1.8) is.
Apply the Runge-Kutta method to approximate this solution on the interval with step size h=0.25. Show five-decimal-place values of the approximate solution and actual solution at the points x=0.25 and 0.5. y'=y-6x-5, y(0)=10; y(x)=11+6x-ex
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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
Use Euler's method to approximate y(1.0). Start with step size h = 0.1, and then use successively smaller step sizes (h= 0.01, 0.001, 0.0001, etc.) until successive approximate solution values at x = 1.0 agree rounded off to two decimal places. y' = x² + y² -1, y(0) = 0 The approximate solution values at x = 1.0 begin to agree rounded off to two decimal places between is (Type an integer or decimal rounded to two decimal places as needed.) So, a good approximation of y(1.0) h = 0.001 and h = 0.0001. h = 0.1 and h=0.01. h = 0.01 and h = 0.001.
Given y' = y cost, 0sts1, y(0) = 1 and N=5. Then using Euler's method, the approximation of the solution at t=0.4 ( use 4 digit rounding) Select one: a. 1.4352 b. 1.4399 с. 1.2216 d. 1.2145
Use a numerical solver and Euler's method to obtain a four-decimal approximation of the indicated value. Use a step size h = 0.2 y'=y-y², y(0)=1.5; y(1) a. y(1)≈ 1.1124 b. y(1) 1.1144 C. y(1)≈ 1.1132 d. y(1) 1.1104 e. y(1) ≈ 1.1102
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
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) = 3; y(x) = 6+3x-3e* Complete the table below. (Round to four decimal places as needed.) ✗n Actual, y (xn) Improved Euler, yn 0.1 0.2 0.3 0.4 0.5
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