Solve the following initial value problem over the interval from x=0 to 1. dy dx = yx2 – 4.5y , where y(0) = 1 a) b) Analytically; Using Euler's method with step sizes h= 0.25. Compare the results obtained by Euler's method with the true values obtained by analytical solution by finding the true percent relative error.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Solve the following initial value problem over the interval from x=0 to 1. Solve the below problem
Solve the following initial value problem over the interval from x=0 to 1.
dy
— ух? — 4.5у ,
dx
where y(0) = 1
%3D
a)
b)
Analytically:
Using Euler's method with step sizes h= 0.25.
Compare the results obtained by Euler's method with the true values obtained by analytical
solution by finding the true percent relative error.
Euler's Methods
Y1+1 = y; + f(xr, , y, )h
Transcribed Image Text:Solve the following initial value problem over the interval from x=0 to 1. dy — ух? — 4.5у , dx where y(0) = 1 %3D a) b) Analytically: Using Euler's method with step sizes h= 0.25. Compare the results obtained by Euler's method with the true values obtained by analytical solution by finding the true percent relative error. Euler's Methods Y1+1 = y; + f(xr, , y, )h
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