1. Use Euler's method with step size 0.50.5 to compute the approximate yy-values y1≈y(0.5), y2≈y(1),y3≈y(1.5), and...

1.

Use Euler's method with step size 0.50.5 to compute the approximate yy-values y1≈y(0.5), y2≈y(1),y3≈y(1.5), and y4≈y(2) of the solution of the initial-value problem

y′=1+3x−2y, y(0)=2.

y1=

y2=

y3=

y4=

2.

Consider the differential equation dy/dx=6x, with initial condition y(0)=3

A. Use Euler's method with two steps to estimate y when x=1:

y(1)≈ (Be sure not to round your calculations at each step!)

Now use four steps:
y(1)≈

B. What is the solution to this differential equation (with the given initial condition)?
y=

C. What is the magnitude of the error in the two Euler approximations you found?
Magnitude of error in Euler with 2 steps =

Magnitude of error in Euler with 4 steps =

D. By what factor should the error in these approximations change (that is, the error with two steps should be what number times the error with four)?
factor =

(How close to this is the result you obtained above?)

Expert Solution

Colby Messinger answered 3 months ago

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1. Use Euler's method with step size 0.50.5 to compute the approximate yy-values y1≈y(0.5), y2≈y(1),y3≈y(1.5), and...

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