Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
For
d
y
d
x
=
x
2
−
y
\dfrac{dy}{dx}=x^{2}-y
d
x
d
y
=
x
2
−
y
with
y
(
0.10
)
=
0.50
y(0.10)=0.50
y
(
0.10
)
=
0.50
, approximate
y
(
0.25
)
y(0.25)
y
(
0.25
)
by taking two successive steps: (i) a step of
Δ
x
=
0.10
\Delta x=0.10
Δ
x
=
0.10
from
x
=
0.10
x=0.10
x
=
0.10
to
x
=
0.20
x=0.20
x
=
0.20
, followed by (ii) a step of
Δ
x
=
0.05
\Delta x=0.05
Δ
x
=
0.05
from
x
=
0.20
x=0.20
x
=
0.20
to
x
=
0.25
x=0.25
x
=
0.25
. Give the final numerical approximation of
y
(
0.25
)
y(0.25)
y
(
0.25
)
.
Browse the problem library