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Byju's Answer
Standard XII
Mathematics
Formation of a Differential Equation from a General Solution
If 饾惒2=a x2+b...
Question
If
y
2
=
a
x
2
+
b
x
+
c
, then
y
3
.
d
2
y
d
x
2
is
A
A constant
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B
A function of x only
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C
A function of y only
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D
A function of x and y
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Solution
The correct option is
A
A constant
y
2
=
a
x
2
+
b
x
+
c
.......... (1)
Differentiate w.r.t x
2
y
y
1
=
2
a
x
+
b
.......... (2)
Diff w.r.t to x
2
y
2
1
+
2
y
y
2
=
2
a
y
2
1
+
y
y
2
=
a
............. (3)
⇒
y
2
y
2
1
+
y
3
y
2
=
a
(
a
x
2
+
b
x
+
c
)
using (2)
⇒
(
a
x
+
b
2
)
2
+
y
3
y
2
=
a
2
x
2
+
a
b
x
+
a
c
⇒
a
2
x
2
+
a
b
x
+
b
2
4
+
y
3
y
2
=
a
2
x
2
+
a
b
x
+
a
c
⇒
y
3
y
2
=
a
c
−
b
2
4
y
3
y
2
=
4
a
c
−
b
2
4
is a constant.
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