1. Homogenous Equation Help

Hey everyone
I'm studying for a test tomorrow, and I need some help with a problem (im sure something of this sort will come up)

$\displaystyle -ydx+(x+\sqrt{xy})dx =0$

im using a substitution, where y = vx, but you still end up with a sqrt with 2 variables in it

thanks

2. Originally Posted by TheUnfocusedOne
Hey everyone
I'm studying for a test tomorrow, and I need some help with a problem (im sure something of this sort will come up)

$\displaystyle -ydx+(x+\sqrt{xy})dx =0$

im using a substitution, where y = vx, but you still end up with a sqrt with 2 variables in it

thanks
I assume you mean (there are two dx differentials):

$\displaystyle -ydx+(x+\sqrt{xy})dy =0$

Rewrite the equation first as:

$\displaystyle -\frac{y}{x}dx+(1+\sqrt{\frac{y}{x}})dy =0$

from which:

$\displaystyle \frac{dy}{dx}=\frac{\frac{y}{x}}{1+\sqrt{\frac{y}{ x}}}$

Then do your proposed substitution as:

$\displaystyle \frac{dy}{dx}=v+x\frac{dv}{dx}=\frac{v}{1+\sqrt{v} }$

Solvable by separation of variables.

Hope this gets you started,

Coomast

3. gah, idiot
i was trying something like that

thanks