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Byju's Answer
Standard XII
Mathematics
Formation of a Differential Equation from a General Solution
If y = sin-...
Question
If
y
=
(
sin
−
1
x
)
2
Then,
(
1
−
x
2
)
d
2
y
d
x
2
−
x
⋅
d
y
d
x
=
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Solution
y
(
sin
−
1
x
)
2
d
y
d
x
=
2
sin
1
x
√
1
−
x
2
√
1
−
x
2
d
y
d
x
=
2
sin
−
1
x
√
1
−
x
2
d
2
y
d
x
2
+
(
−
x
√
1
−
x
2
)
d
y
d
x
=
2
√
1
−
x
2
(
1
−
x
2
)
d
2
y
d
x
2
−
x
d
y
d
x
=
2
.
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Similar questions
Q.
If
y
=
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s
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−
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x
)
2
+
(
c
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t
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(
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If
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, then
(
1
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d
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Q.
If
y
=
(
sin
−
1
x
)
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, then show that
(
1
−
x
2
)
d
2
y
d
x
2
−
x
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x
=
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Q.
If
y
=
(
sin
−
1
x
)
2
, then prove that
(
1
−
x
2
)
d
2
y
d
x
2
−
x
d
y
d
x
=
2
.
Q.
If
y
=
(
sin
−
1
x
)
2
+
c
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then prove that
(
1
−
x
2
)
d
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=
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Formation of a Differential Equation from a General Solution
Standard XII Mathematics
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