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\[\large ({{y \over x} + e^{-xy}})dx + dy =0\]

It doesn't look seperable, I still have y in the exponent of the dx term

you did partial differentiation...but I'm not quite sure of what

not yet

only homogenous diff. eq, and substitution

I get how you got that...but how does writing it as dy/dx help?

It's to show how it's not homogeneous.

how can you tell it's not homogeneous?

\[\large y(1)=0\]

Does \(\frac{ty}{tx}+e^{-(tx)(ty)}=\frac{y}x+e^{-xy}\)?

I don't know? That was an Intial condition that I forgot to type...

Do you know how to test whether an ODE is homogeneous?

ODE? I'm guesing DE is diff. eq.

ordinary differential equation

no clue

So you haven't learned about homogeneous differential equations?

homogeneous yes, ordinary, not a term we've used

Ordinary is on contrast with partial differential equations, where you have partial derivatives.

you realize that I'm totally confused right? this is only my second class meeting

:-p ok well tell me what you've been taught so far.

just separating the terms and substitution if the equation can't be solved on the spot

Hope this helps.

... are you seriously just posting links to what Mathematica or Wolfram|Alpha spits out?

Yes.