Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
If a curve
y
=
f
(
x
)
y = f(x)
y
=
f
(
x
)
, passing through the point
(
1
,
2
)
(1, 2)
(
1
,
2
)
, is the solution of the differential equation,
2
x
2
d
y
=
(
2
x
y
+
y
2
)
d
x
2x^2 dy = (2xy + y^2)dx
2
x
2
d
y
=
(
2
x
y
+
y
2
)
d
x
, then
f
(
1
2
)
f\left(\frac{1}{2}\right)
f
(
2
1
)
is equal to (a)
1
1
+
log
e
2
\frac{1}{1 + \log_e 2}
1
+
l
o
g
e
2
1
(b)
1
1
−
log
e
2
\frac{1}{1 - \log_e 2}
1
−
l
o
g
e
2
1
(c)
1
+
log
e
2
1 + \log_e 2
1
+
lo
g
e
2
(d)
−
1
1
+
log
e
2
\frac{-1}{1 + \log_e 2}
1
+
l
o
g
e
2
−
1
Browse the problem library