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Engineering Mathematics
Variables Separable Method I
Consider the ...
Question
Consider the differential equation
d
y
d
x
=
(
1
+
y
2
)
x
The general solution with constant c is
A
y = tan
x
2
2
+
t
a
n
c
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B
y
=
t
a
n
2
(
x
2
+
c
)
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C
y
=
t
a
n
2
(
x
2
)
+
c
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D
y
=
t
a
n
(
x
2
2
+
c
)
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Solution
The correct option is
D
y
=
t
a
n
(
x
2
2
+
c
)
Given
d
y
d
x
=
(
1
+
y
2
)
x
d
y
1
+
y
2
=
x
d
x
Integrating, we get
∫
d
y
1
+
y
2
=
∫
x
d
x
t
a
n
−
1
(
y
)
=
x
2
2
+
c
⇒
y
=
t
a
n
(
x
2
2
+
c
)
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