# seperation of variables

• July 18th 2007, 02:59 PM
geode
seperation of variables
Help! :confused: I can't figure out this problem:

Find f(x), when cos^2(x)f'(x) = e^-f(x), and f(0) = 0.5

I have several other questions which I am lost on so I will be posting several! Thanks!
• July 18th 2007, 03:29 PM
ThePerfectHacker
Quote:

Originally Posted by geode
Help! :confused: I can't figure out this problem:

Find f(x), when cos^2(x)f'(x) = e^-f(x), and f(0) = 0.5

I have several other questions which I am lost on so I will be posting several! Thanks!

Let say we want to solve,
$\cos^2 x f'(x) = e^{-f(x)} \mbox{ on }(0,\pi/2)$
Then,
$\frac{f'(x)}{e^{-f(x)}} = \sec^2 x$

This is a seperable differencial equation.