Sunday, March 23, 2014

What is dy/dx for y - ln(1/y) + ln(y) = ln(x).

We have y - ln ( 1/y) + ln y = ln
x


use the relation that log a  + log b = log
a*b


=> y - ln [( 1/y)(1/y)] = ln
x


=> y - ln [ 1/y^2] = ln
x


=> dy/dx - y^2*(-2)*(1/y^3)*dy/dx =
1/x


=> dy/dx [ 1 + 2* y^2 / y^3] =
1/x


=> dy/dx [ 1 + 2/y]=
1/x


=> dy/dx  = 1/[x*(1 +
2/y)]


The required value of dy/dx  = 1/[x*(1
+ 2/y)]

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