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August 28, 2014

August 28, 2014

Posted by **daria** on Sunday, March 30, 2008 at 1:40am.

Show that y=loge(logex) is a solution of the equation

xd^2y/dx^2 + x(dy/dx)^2 + dy/dx=o

- calculus -
**drwls**, Sunday, March 30, 2008 at 3:07amThe first derivative of ln (ln x) is dy/dx = 1/(x*ln x)

The second derivative is:

d^2y/dx^2 = [-ln x/x^2 - (1/x^2)]/(ln x)^2

= -1/(x^2 ln x) -1/(x ln x)^2

x d^2y/dx^2 = -1/(x ln x) - (1/x)/lnx^2

It seems to fit the differential equation

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