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Byju's Answer
Standard XII
Mathematics
Bernoulli's Equation
The solution ...
Question
The solution of the differential equation
d
y
d
x
=
a
x
+
g
b
y
+
f
represents a circle when
(a) a = b
(b) a = −b
(c) a = −2b
(d) a = 2b
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Solution
(b) a = −b
We have,
d
y
d
x
=
a
x
+
g
b
y
+
f
⇒
b
y
+
f
d
y
=
a
x
+
g
d
x
Integrating
both
sides
,
we
get
∫
b
y
+
f
d
y
=
∫
a
x
+
g
d
x
⇒
b
y
2
2
+
f
y
=
a
x
2
2
+
g
x
+
C
⇒
b
y
2
2
+
f
y
-
a
x
2
2
-
g
x
=
C
⇒
b
y
2
+
2
f
y
-
a
x
2
-
2
g
x
-
2
C
=
0
The
above
equation
represents
a
circle
.
Therefore
,
the
coffecients
of
x
2
and
y
2
must
be
equal
.
i
.
e
.
-
a
=
b
⇒
a
=
-
b
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