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Question
Mathematics
Consider the differential equation ((2+ sin x/y+1)) (d y/d x)=- cos x If y(0)=1, then evaluate 6 y((π/2))+5
Q. Consider the differential equation
(
y
+
1
2
+
s
i
n
x
)
d
x
d
y
=
−
cos
x
If
y
(
0
)
=
1
, then evaluate
6
y
(
2
π
)
+
5
884
154
Differential Equations
Report Error
Answer:
7
Solution:
(
y
+
1
2
+
s
i
n
x
)
d
x
d
y
=
−
cos
x
⇔
y
+
1
d
y
=
2
+
s
i
n
x
−
c
o
s
x
d
x
Integrating, we get
lo
g
(
y
+
1
)
=
−
lo
g
(
2
+
sin
x
)
−
lo
g
k
⇒
k
(
y
+
1
)
(
2
+
sin
x
)
=
1
y
(
0
)
=
1
⇒
k
=
4
1
⇒
(
y
+
1
)
(
2
+
sin
x
)
=
4
At
x
=
2
π
(
y
+
1
)
(
3
)
=
4
⇒
y
(
2
π
)
=
3
1
⇒
6
y
(
2
π
)
+
5
=
7