## qrious126 one year ago How would you go about solving this equation?

1. qrious126

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

2. qrious126

@UnkleRhaukus

3. qrious126

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

4. qrious126

@dan815

5. UnkleRhaukus

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

6. qrious126

cool. thanks!

7. whpalmer4

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

8. UnkleRhaukus

ah yes, thanks for spotting that @whpalmer4

9. qrious126

yes, just noticed. thanks!