Here is the problem:(adsbygoogle = window.adsbygoogle || []).push({});

Determine the orthogonal trajectories of the given family of curves.

[tex] y = \sqrt{2\ln{|x|}+C} [/tex]

This is what I've done so far:

[tex] y = (2\ln{|x|}+C)^\frac{-1}{2} [/tex]

[tex] y' = -1/2(2\ln{|x|+C)(2/x) [/tex]

Now I understand to find the orthogonal lines I need to divide -1 by whatever I get, the problem is, I can't simplify this derivative.

I've messed around with it a bit, and I have this:

[tex] -(2\ln{|x|}+C)/x [/tex]

How else can I simplify this?

Thanks.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Diff Eq problem

**Physics Forums | Science Articles, Homework Help, Discussion**