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Mathematics
Mathematics
Problem
Let
y
=
f
(
x
)
y = f(x)
y
=
f
(
x
)
be the solution to the differential equation
d
y
d
x
=
x
−
y
\frac{dy}{dx} = x - y
d
x
d
y
=
x
−
y
with initial condition
f
(
1
)
=
3
f(1) = 3
f
(
1
)
=
3
. What is the approximation for
f
(
2
)
f(2)
f
(
2
)
obtained by using Euler's method with two steps of equal length starting at
x
=
1
x = 1
x
=
1
?
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