Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
If for the solution curve
y
=
f
(
x
)
y = f(x)
y
=
f
(
x
)
of the differential equation
d
y
d
x
+
(
tan
x
)
y
=
2
+
sec
x
(
1
+
2
sec
x
)
2
,
x
∈
(
−
π
2
,
π
2
)
,
\frac{dy}{dx} + (\tan x) y = \frac{2 + \sec x}{(1 + 2 \sec x)^2}, \quad x \in \left(-\frac{\pi}{2}, \frac{\pi}{2}\right),
d
x
d
y
+
(
tan
x
)
y
=
(
1
+
2
sec
x
)
2
2
+
sec
x
,
x
∈
(
−
2
π
,
2
π
)
,
f
(
π
3
)
=
3
10
f\left(\frac{\pi}{3}\right) = \frac{\sqrt{3}}{10}
f
(
3
π
)
=
10
3
, then
f
(
π
4
)
f\left(\frac{\pi}{4}\right)
f
(
4
π
)
is equal to : (a)
9
3
+
3
10
(
4
+
3
)
\frac{9\sqrt{3} + 3}{10(4 + \sqrt{3})}
10
(
4
+
3
)
9
3
+
3
(b)
3
+
1
10
(
4
+
3
)
\frac{\sqrt{3} + 1}{10(4 + \sqrt{3})}
10
(
4
+
3
)
3
+
1
(c)
5
−
3
2
2
\frac{5 - \sqrt{3}}{2\sqrt{2}}
2
2
5
−
3
(d)
4
−
2
14
\frac{4 - \sqrt{2}}{14}
14
4
−
2
Browse the problem library