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3. Use Euler's method to approximate the value of = -2x3 + 12x2 - 20x +8.5 from x = 0 to x = 4. The initial condition is y(0) = 1. Use the following step size: a. h= 0.5 b. h = 0.25 C. h=0.1 d. Compute for the true error and relative percentage error using the true value of y = -0.5x* + 4x3 + 8.5x + 1 at x-4 for each given steps.

3. Use Euler's method to approximate the value of = -2x3 + 12x2 - 20x +8.5 from x = 0 to x = 4. The initial condition is y(0) = 1. Use the following step size: a. h= 0.5 b. h = 0.25 C. h=0.1 d. Compute for the true error and relative percentage error using the true value of y = -0.5x* + 4x3 + 8.5x + 1 at x-4 for each given steps.

Advanced Engineering Mathematics
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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3. Use Euler's method to approximate the value of = -2x3 + 12x2 - 20x + 8.5 from x = 0 to x = 4. The initial condition is y(0) = 1. Use the following step size: a. h= 0.5 dx b. h 0.25 C. h 0.1 d. Compute for the true error and relative percentage error using the true value of y = -0.5x* + 4x3 + 8.5x + 1 at x-4 for each given steps. 1. Ka Ping has decided to save money roughly P100 per week. Suppose he makes a bi-monthly deposits of this money into a bank account that pays annual interest of 10%, compounded continuously. Use annuity formula: = rS + d; S(0) = So ds %3D dt a. Use Euler's method and approximate the balance after 4 years. b. Solve the general solution of the given annuity formula and solve for the exact value. 3 dy 2. 32+5y = sin x, y(0.3)= 5 and using a step size of h = 0.3, Approximate the value of y(0.9) dx using Euler's method.
Transcribed Image Text:3. Use Euler's method to approximate the value of = -2x3 + 12x2 - 20x + 8.5 from x = 0 to x = 4. The initial condition is y(0) = 1. Use the following step size: a. h= 0.5 dx b. h 0.25 C. h 0.1 d. Compute for the true error and relative percentage error using the true value of y = -0.5x* + 4x3 + 8.5x + 1 at x-4 for each given steps. 1. Ka Ping has decided to save money roughly P100 per week. Suppose he makes a bi-monthly deposits of this money into a bank account that pays annual interest of 10%, compounded continuously. Use annuity formula: = rS + d; S(0) = So ds %3D dt a. Use Euler's method and approximate the balance after 4 years. b. Solve the general solution of the given annuity formula and solve for the exact value. 3 dy 2. 32+5y = sin x, y(0.3)= 5 and using a step size of h = 0.3, Approximate the value of y(0.9) dx using Euler's method.
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