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Mathematics
Mathematics
Problem
If
x
=
∫
0
y
d
t
1
+
t
2
x = \int_{0}^{y} \frac{dt}{\sqrt{1+t^2}}
x
=
∫
0
y
1
+
t
2
d
t
, then
d
2
y
d
x
2
\frac{d^2y}{dx^2}
d
x
2
d
2
y
is equal to : (1)
y
2
y^2
y
2
(2)
y
1
+
y
2
\frac{y}{\sqrt{1+y^2}}
1
+
y
2
y
(3)
y
y
y
(4)
1
+
y
2
\sqrt{1+y^2}
1
+
y
2
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