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Joint Entrance Examination
Mathematics
Differential Equations
Question 316
Question 316 of 490
Easy
MCQ
If
d
y
d
x
=
y
+
3
>
0
\dfrac{dy}{dx}=y+3>0
d
x
d
y
=
y
+
3
>
0
,
y
(
0
)
=
2
y(0)=2
y
(
0
)
=
2
, then
y
(
ln
2
)
y(\ln2)
y
(
ln
2
)
is:
A
5
B
13
C
-2
D
7
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Official solution
ln
∣
y
+
3
∣
=
x
+
ln
5
\ln|y+3|=x+\ln5
ln
∣
y
+
3∣
=
x
+
ln
5
. At
x
=
ln
2
x=\ln2
x
=
ln
2
:
ln
∣
y
+
3
∣
=
ln
10
⟹
y
+
3
=
10
⟹
y
=
7
\ln|y+3|=\ln10 \implies y+3=10 \implies y=7
ln
∣
y
+
3∣
=
ln
10
⟹
y
+
3
=
10
⟹
y
=
7
.
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