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Joint Entrance Examination
Mathematics
Differential Equations
Question 164
Question 164 of 490
Medium
MCQ
Let
y
=
y
1
(
x
)
y=y_1(x)
y
=
y
1
(
x
)
and
y
=
y
2
(
x
)
y=y_2(x)
y
=
y
2
(
x
)
solve
d
y
d
x
=
y
+
7
\dfrac{dy}{dx}=y+7
d
x
d
y
=
y
+
7
with
y
1
(
0
)
=
0
y_1(0)=0
y
1
(
0
)
=
0
,
y
2
(
0
)
=
1
y_2(0)=1
y
2
(
0
)
=
1
. The curves intersect at:
A
no point
B
infinite number of points
C
one point
D
two points
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Solutions · 1
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Official solution
y
=
−
7
+
c
e
x
y=-7+ce^x
y
=
−
7
+
c
e
x
;
y
1
y_1
y
1
:
c
=
7
c=7
c
=
7
,
y
2
y_2
y
2
:
c
=
8
c=8
c
=
8
. Setting
y
1
=
y
2
y_1=y_2
y
1
=
y
2
:
7
e
x
=
8
e
x
⇒
e
x
=
0
7e^x=8e^x \Rightarrow e^x=0
7
e
x
=
8
e
x
⇒
e
x
=
0
, impossible --- no intersection.
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