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Byju's Answer
Standard XII
Mathematics
Continuity of a Function
Solve the fol...
Question
Solve the following
y
√
1
+
x
2
+
x
√
1
+
y
2
d
y
d
x
=
0
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Solution
y
√
1
+
x
2
+
x
√
1
+
y
2
d
y
d
x
=
0
⇒
x
√
1
+
y
2
d
y
d
x
=
−
y
√
1
+
x
2
⇒
√
1
+
y
2
d
y
y
=
−
√
1
+
x
2
d
x
x
integrating both sides
⇒
∫
√
1
+
y
2
d
y
y
=
−
∫
√
1
+
x
2
d
x
x
Let
y
=
tan
θ
,
=
∫
√
1
+
tan
2
θ
tan
θ
.
sec
2
θ
d
θ
=
∫
sec
3
θ
tan
θ
d
θ
=
∫
sec
2
sin
θ
d
θ
=
∫
sec
2
θ
csc
θ
d
θ
=
∫
sec
2
θ
d
θ
+
∫
csc
2
θ
d
θ
=
tan
θ
−
cot
θ
=
y
−
1
y
∴
∫
√
1
+
y
2
d
y
y
=
−
∫
√
1
+
x
2
d
x
x
y
−
1
y
=
−
(
x
−
1
x
)
+
c
y
2
−
1
y
=
1
−
x
2
x
+
c
Hence, solved.
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Q.
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)
d
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+
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Q.
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Q.
Reduce each of the following differential equations to the variables separable form and hence solve .
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Q.
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x
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+
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