Question

How would you go about solving this equation?

Answer 1

\[xy \prime - y = 2(xy)^{1/2}\]

Answer 2

@UnkleRhaukus

Answer 3

i know u can use both the homogeneous approach and the Bernoulli method here, but i cant seem to get the right answer.

Answer 4

@dan815

Answer 5

\[xy^\prime - y = 2(xy)^{1/2}\\y'=\frac{2(xy)^{1/2}-y}x\\=2(y/x)^{1/2}-y/x\]

Answer 6

cool. thanks!

Answer 7

Uh, there's a mistake in there, I'm afraid...
\[xy' - y = 2(xy)^{1/2}\]
xy' = 2(xy)^{1/2}+y\]
\[y' = \frac{2(xy)^{1/2}+y}{x} = 2(y/x)^{1/2}\color{red}{+}y/x\]

Answer 8

ah yes, thanks for spotting that @whpalmer4

Answer 9

yes, just noticed. thanks!