Section
2.7
Euler
Method:
Problem
2
(1
point)
Consider
the
differential
equation
&
=%
au
X
with
initial
condition
y(0)
=
5.
A.
Use
Euler's
method
with
two
steps
to
estimate
y
when
x
=
1:
W0
=
(575
(Be
sure
not
to
round
your
calculations
at
each
step!)
Now
use
four
steps:
=
(6120
(Be
sure
not
to
round
your
calculations
at
each
step!)
B.
What
is
the
solution
to
this
differential
equation
(with
the
given
initial
condition)?
2
—
|
3x_
y
B
H
C.
What
is
the
magnitude
of
the
error
in
the
two
Euler
approximations
you
found?
Magnitude
of
error
in
Euler
with
2
steps
=|
.75
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?)
