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Mathematics
Mathematics
Problem
If
y
=
A
cos
(
log
x
)
+
B
sin
(
log
x
)
y = A \cos(\log x) + B \sin(\log x)
y
=
A
cos
(
lo
g
x
)
+
B
sin
(
lo
g
x
)
, then prove that
x
2
d
2
y
d
x
2
+
x
d
y
d
x
+
y
=
0
x^2 \frac{d^2 y}{dx^2} + x \frac{dy}{dx} + y = 0
x
2
d
x
2
d
2
y
+
x
d
x
d
y
+
y
=
0
.
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