what's the general solution?

x*y*y' = y^2 + x*sqrt(4*x^2 + y^2)

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- September 9th 2010, 11:42 PMfryfrygeneral solution of this differential equation?
what's the general solution?

x*y*y' = y^2 + x*sqrt(4*x^2 + y^2) - September 10th 2010, 03:45 AMmr fantastic
- September 10th 2010, 04:07 AMAckbeet
I'm not sure I quite agree. I get

That last equality comes from the DE, from arranging the LHS to look like what's in the parentheses. At this point, you could make the substitution

I was thinking quotient rule for derivatives, but was getting hung up on not having the x squared term in the denominator, which you have to have in order to make the coefficients the same in the numerator. - September 10th 2010, 04:17 AMmr fantastic
- September 10th 2010, 05:32 AMAckbeet
Fair enough. I think the previous lack of equals sign was throwing me off.

- September 10th 2010, 08:57 AMzzzoak

May be this way is good

(1)

The initial equation becomes

From (1) get y.