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Mathematics
Mathematics
Problem
If
y
=
x
log
(
x
a
+
b
x
)
y = x \log \left( \frac{x}{a+bx} \right)
y
=
x
lo
g
(
a
+
b
x
x
)
, then prove that
x
3
d
2
y
d
x
2
=
(
x
d
y
d
x
−
y
)
2
x^3 \frac{d^2 y}{dx^2} = \left( x \frac{dy}{dx} - y \right)^2
x
3
d
x
2
d
2
y
=
(
x
d
x
d
y
−
y
)
2
.
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