Consider the differential equation:
d
y
d
x
=
5
x
...
Mathematics, 24.01.2022 16:00 ethangeibel93
Consider the differential equation:
d
y
d
x
=
5
x
with initial condition y(0)=1.
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)?
(Be sure not to round your calculations at each step!)
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?
The magnitude of error in Euler with 2 steps =
The 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 =
Please answer in detail. I am making an error somewhere.
Thanks!!
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