# 1st order homogeneous

• May 21st 2011, 11:31 AM
ychana
1st order homogeneous
Hi guys,

I was trying to solve $\frac{ds}{dt} = \frac{-2s^2}{s^2 + t^2}$. Normally I do not struggle at these problems but I cannot get it into the form $f(\frac{s}{t})$.

Any help would be much appreciated!

Ychana
• May 21st 2011, 11:34 AM
TheEmptySet
Quote:

Originally Posted by ychana
Hi guys,

I was trying to solve $\frac{ds}{dt} = \frac{-2s^2}{s^2 + t^2}$. Normally I do not struggle at these problems but I cannot get it into the form $f(\frac{s}{t})$.

Any help would be much appreciated!

Ychana

Hint:

$\frac{-2s^2}{s^2+t^2}=\frac{s^2}{s^2}\cdot \frac{-2}{1+\left( \frac{t}{s}\right)^2}=\frac{-2}{1+\left( \frac{t}{s}\right)^2}$