1. Using h = 0.5, approximate the value of y(3) for the given differential equation using a) Euler method, b) Improved Euler method, and c) 4th order Runge-Kutta method. Show your solutions for the first, third and last row. Box the final answer. No rounding off computed values. (x³ + y) dx dy = 0 y(0) = 1

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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1. Using h = 0.5, approximate the value of y(3) for the given differential equation using a) Euler
method, b) Improved Euler method, and c) 4th order Runge-Kutta method. Show your solutions
for the first, third and last row. Box the final answer. No rounding off computed values.
(x³ + y) dx dy = 0
y(0) = 1
2. Using h = 0.1, approximate the value of y(0.5) for the given differential equation using a) Euler
method, b) Improved Euler method, and c) 4th order Runge-Kutta method. Show your solutions
for the first, third and last row. Box the final answer. No rounding off computed values.
y' = y + 2x - x² y(0) = 1
Transcribed Image Text:1. Using h = 0.5, approximate the value of y(3) for the given differential equation using a) Euler method, b) Improved Euler method, and c) 4th order Runge-Kutta method. Show your solutions for the first, third and last row. Box the final answer. No rounding off computed values. (x³ + y) dx dy = 0 y(0) = 1 2. Using h = 0.1, approximate the value of y(0.5) for the given differential equation using a) Euler method, b) Improved Euler method, and c) 4th order Runge-Kutta method. Show your solutions for the first, third and last row. Box the final answer. No rounding off computed values. y' = y + 2x - x² y(0) = 1
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