what's the general solution?
x*y*y' = y^2 + x*sqrt(4*x^2 + y^2)
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.