Question

find the general solution:
yy'=-x+((x^2)+(y^2))^0.5

Answer 1

Note first that (y^2)' = 2yy' and (x^2)' = 2x

Thus

(y^2 + x^2)' = 2yy' + 2x

Hence if we let u = x^2 + y^2, we can rewrite your equation as

1/2 . u' = u^(1/2)

Now you can solve that equation by separation of variables.