Can anyone help with any of these?

Yes, so the equilibrium cases are when y' = 0, so x = +-1,y= reals as well as y=1, x = reals.

bump

For some reason it wont let me post my asnwer

Test post
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wow I cant post my answer, keep getting connection error. I swear my prof is a mod

any advice for 4?

Not that guy but fuck it. It's five fucking thirty AM and I need sleep, so I'll just give you the rough jist which I think leads to the answer.

For (i, substitute u = y^{-2} like you're given into the result you should be getting. Apply chain rule, du/dx = (du/dy)(dy/dx) = (du/dy) y'. At the end you'll need to multiply by some power of y to get the ODE a is given in terms of y. Just write this whole process backwards if need be, there's your answer.

For (ii) multiply the ODE in terms of u(y) through by x and you should immediately see it's a nonhomogenous first order Cauchy-Euler equation. Solve homogenous problem proposing solution of the form u(y(x)) = Cx^{-m}, then apply variation of parameters to solve your nonhomogenous problem.

(iii) is kinda trivial. Do it yourself, nigger.

Thanks user ill give it a go

Read a textbook or chuck it into Wolfram Alpha if you're a nigger.

>wolfram alpha

That just plugs and chugs, doesnt always help