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Consider the initial value problem dy = x - y², y(0) = 1 dx (a) Use the modified Euler method with step h = 0.1 to determine the approximate value of the solution at x = 0.1. Give the answer correct to the fourth decimal place. (b) Use the fourth order Runge-Kutta method with step h = 0.5 to determine the approximate value of the solution at x = 0.5. Give the answer correct to the fourth decimal place.

Consider the initial value problem dy = x - y², y(0) = 1 dx (a) Use the modified Euler method with step h = 0.1 to determine the approximate value of the solution at x = 0.1. Give the answer correct to the fourth decimal place. (b) Use the fourth order Runge-Kutta method with step h = 0.5 to determine the approximate value of the solution at x = 0.5. Give the answer correct to the fourth decimal place.

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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Consider the initial value problem dy %3D х — у?, у(0) %3D 1 dx (a) Use the modified Euler method with step h = 0.1 to determine the approximate value of the solution at x = 0.1. Give the answer correct to the fourth decimal place. (b) Use the fourth order Runge-Kutta method with step h = 0.5 to determine the approximate value of the solution at x = 0.5. Give the answer correct to the fourth decimal place.
Transcribed Image Text:Consider the initial value problem dy %3D х — у?, у(0) %3D 1 dx (a) Use the modified Euler method with step h = 0.1 to determine the approximate value of the solution at x = 0.1. Give the answer correct to the fourth decimal place. (b) Use the fourth order Runge-Kutta method with step h = 0.5 to determine the approximate value of the solution at x = 0.5. Give the answer correct to the fourth decimal place.
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