I'm pretty sure I'm doing something wrong.

the question is:

Formulate the general solution to the differential equation. (express in y^2 in terms of x)

This is what I did doing so far.

the final answer just looks way too weird.

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- Feb 5th 2011, 10:30 AMkonvosHaving problem with this separation
I'm pretty sure I'm doing something wrong.

the question is:

Formulate the general solution to the differential equation. (express in y^2 in terms of x)

This is what I did doing so far.

the final answer just looks way too weird. - Feb 5th 2011, 10:44 AMTheEmptySet
- Feb 5th 2011, 11:23 AMAckbeet
Just as a further explanation of TheEmptySet's post: the original DE is Bernoulli, and hence a substitution of the form will render the equation linear in

- Feb 5th 2011, 11:26 AMkonvos
Thx for the help.

The Y^2 is getting my confused. The formula I'm applying is

http://upload.wikimedia.org/math/4/d...72eec8acb7.png

applying to both sides, I should get

I just guessed that the y^2 would be squared, I tried looking for a example in my book and I couldn't find.

so the final answer is :

but like I said... I just guessed on the y^2, so i'm not sure - Feb 5th 2011, 11:30 AMAckbeet
Why are you applying that formula, when it doesn't apply? That formula is the form of a first-order linear DE, but that's not what you start out with. If you will employ TheEmptySet's substitution, you will get a first-order linear DE in u, at which point you can employ the integrating factor method.

- Feb 5th 2011, 11:42 AMkonvos
- Feb 5th 2011, 11:54 AMTheEmptySet