Consider the following. Differential Equation dy 2x + 12 dx 3y² - 4 = Initial Condition x-value X (1, 2) (a) Use Euler's Method with a step size of h = 0.1 to approximate the particular solution of the initial value problem at the given x-value. (Round your answer to four decimal places.) y = 3.0318 x = 2 (b) Find the exact solution of the differential equation analytically. (Enter your solution as an equation.) y³ - 12y-50=0 (c) Find the error between Euler's Method and the exact solution by comparing the solutions at the given x-value. (Round your answer to four decimal places.) 0.0126 X
Consider the following. Differential Equation dy 2x + 12 dx 3y² - 4 = Initial Condition x-value X (1, 2) (a) Use Euler's Method with a step size of h = 0.1 to approximate the particular solution of the initial value problem at the given x-value. (Round your answer to four decimal places.) y = 3.0318 x = 2 (b) Find the exact solution of the differential equation analytically. (Enter your solution as an equation.) y³ - 12y-50=0 (c) Find the error between Euler's Method and the exact solution by comparing the solutions at the given x-value. (Round your answer to four decimal places.) 0.0126 X
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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Transcribed Image Text:Consider the following.
Differential Equation
dy
2x + 12
dx 3у2 - 4
Initial Condition
(a) Use Euler's Method with a step size of h
=
(Round your answer to four decimal places.)
y = 3.0318
'y
(1, 2)
- 12y - 50=0
x-value
(b) Find the exact solution of the differential equation analytically. (Enter your solution as an equation.)
3
X
X = 2
0.1 to approximate the particular solution of the initial value problem at the given x-value.
(c) Find the error between Euler's Method and the exact solution by comparing the solutions at the given x-value. (Round your answer to
four decimal places.)
0.0126
X
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