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Exams
Joint Entrance Examination
Mathematics
Differential Equations
Question 317
Question 317 of 490
Medium
MCQ
Consider
y
2
d
x
+
(
x
−
1
y
)
d
y
=
0
y^2\,dx+\left(x-\dfrac1y\right)dy=0
y
2
d
x
+
(
x
−
y
1
)
d
y
=
0
. If
y
(
1
)
=
1
y(1)=1
y
(
1
)
=
1
, then
x
x
x
is given by:
A
4
−
2
y
−
e
1
/
y
e
4-\dfrac2y-\dfrac{e^{1/y}}{e}
4
−
y
2
−
e
e
1/
y
B
3
−
1
y
+
e
1
/
y
e
3-\dfrac1y+\dfrac{e^{1/y}}{e}
3
−
y
1
+
e
e
1/
y
C
1
+
1
y
−
e
1
/
y
e
1+\dfrac1y-\dfrac{e^{1/y}}{e}
1
+
y
1
−
e
e
1/
y
D
1
−
1
y
+
e
1
/
y
e
1-\dfrac1y+\dfrac{e^{1/y}}{e}
1
−
y
1
+
e
e
1/
y
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Solutions · 1
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Official solution
(Same ODE structure as Question 220.) With I.F.
=
e
−
1
/
y
=e^{-1/y}
=
e
−
1/
y
, solving with
y
(
1
)
=
1
y(1)=1
y
(
1
)
=
1
gives
x
=
1
+
1
y
−
e
1
/
y
e
x=1+\dfrac1y-\dfrac{e^{1/y}}{e}
x
=
1
+
y
1
−
e
e
1/
y
.
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