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!!