I have no idea how to do these. And we *have* to do it as a Bernoulli equation.
Initial values: (0, 1/3)
The procedure is given here (and no doubt it's in your classnotes and textbook too): Bernoulli differential equation - Wikipedia, the free encyclopedia
What part of applying this procedure are you stuck on?
http://www.wolframalpha.com/input/?i...+xy+%3D+xy%5E3
The DE is seperable in fact. Are you required to do it as a Bernoulli?
There are a number of things you are not doing correctly. Have you read any references on the required technique eg. http://en.wikipedia.org/wiki/Bernoul...ntial_equation.
Please show all your work, every step, so that it can be reviewed.
Getting integrating factor.
Did the integration in my head. You integrate [e^-x^/2(u)}]' and -2xe^{-x^2}. It's easy to see on the right side the -2x term will cancel out by u-substitution.
Sub in the u.
Plug in initial values to this equation. Y(0) = 1/3
And yes, I read your first reference to wikipedia, but I got the first answer I posted yesterday as that weird square root. Then, I tried looking for examples.