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Mathematics
Mathematics
Problem
Let
y
=
y
(
x
)
y = y(x)
y
=
y
(
x
)
be the solution of the differential equation
d
y
d
x
+
3
(
tan
2
x
)
y
+
3
y
=
sec
2
x
\frac{dy}{dx} + 3(\tan^2 x)y + 3y = \sec^2 x
d
x
d
y
+
3
(
tan
2
x
)
y
+
3
y
=
sec
2
x
y
(
0
)
=
1
3
+
e
3
y(0) = \frac{1}{3} + e^3
y
(
0
)
=
3
1
+
e
3
. Then
y
(
π
4
)
y\left(\frac{\pi}{4}\right)
y
(
4
π
)
is equal to
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