dw
dx  = w (1 + log x)
= xx (1 + log x) (4)
From (1), (2), (3), (4), we have
log
log
x
y
x dy
y
dy
y
y
x
x
y dx
x
dx




+
+
+








 + xx (1 + log x) = 0
or
(x yx – 1 + xy log x) dy
dx  = – xx (1 + log x) – y