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Joint Entrance Examination
Mathematics
Differential Equations
Question 312
Question 312 of 490
Easy
MCQ
The integrating factor of
(
x
2
−
1
)
d
y
d
x
+
2
x
y
=
x
(x^2-1)\dfrac{dy}{dx}+2xy=x
(
x
2
−
1
)
d
x
d
y
+
2
x
y
=
x
is:
A
1
x
2
−
1
\dfrac{1}{x^2-1}
x
2
−
1
1
B
x
2
−
1
x^2-1
x
2
−
1
C
x
2
−
1
x
\dfrac{x^2-1}{x}
x
x
2
−
1
D
x
x
2
−
1
\dfrac{x}{x^2-1}
x
2
−
1
x
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Official solution
d
y
d
x
+
2
x
x
2
−
1
y
=
x
x
2
−
1
\dfrac{dy}{dx}+\dfrac{2x}{x^2-1}y=\dfrac{x}{x^2-1}
d
x
d
y
+
x
2
−
1
2
x
y
=
x
2
−
1
x
; I.F.
=
e
∫
2
x
x
2
−
1
d
x
=
x
2
−
1
=e^{\int\frac{2x}{x^2-1}dx}=x^2-1
=
e
∫
x
2
−
1
2
x
d
x
=
x
2
−
1
.
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