give first the step you will use to separate the variable and then solve the equations (e) y - 4= -7
Answers
Answered by
0
Answer:
This is an example of a separable equation with an initial value.
d
y
d
x
=
e
−
y
(
2
x
−
4
)
y
(
5
)
=
0
by multiplying by
e
y
and by
d
x
,
⇒
e
y
d
y
=
(
2
x
−
4
)
d
x
by integrating,
⇒
∫
e
y
d
y
=
∫
(
2
x
−
4
)
d
x
⇒
e
y
=
x
2
−
4
x
+
C
by taking the natural log,
⇒
y
=
ln
(
x
2
−
4
x
+
C
)
Now, we need to find
C
using
y
(
5
)
=
0
.
y
(
5
)
=
ln
(
(
5
)
2
−
4
(
5
)
+
C
)
=
ln
(
5
+
C
)
=
0
⇒
5
+
C
=
1
⇒
C
=
−
4
Hence, the solution is
y
=
ln
(
x
2
−
4
x
−
4
)
.
Answered by
5
Answer:
y=11
Explanation:
y-4=-7
y=7+4
y=11
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