Diff EQs : Need help setting up an equation for direct substitution...

So the given ODE is: $$y'=y+y ^{-1}$$ and I'm supposed to use direct substitution to make this a first order differential equation.

I tried combining the right hand side like so: $$\frac{ y ^{2}+1 }{ y }$$ but I don't know if thats right because now Im stuck. Any suggestios?

Question

Diff EQs : Need help setting up an equation for direct substitution...

So the given ODE is: $$y'=y+y ^{-1}$$ and I'm supposed to use direct substitution to make this a first order differential equation. 

I tried combining the right hand side like so: $$\frac{ y ^{2}+1 }{ y }$$ but I don't know if thats right because now Im stuck. Any suggestios?

adunb8 · Answer

try using Bernoulli's equation? perhaps?

anonymous · Answer

im having trouble getting it into that form.