qrious126
How would you go about solving this equation?



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qrious126
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\[xy \prime  y = 2(xy)^{1/2}\]

qrious126
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@UnkleRhaukus

qrious126
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i know u can use both the homogeneous approach and the Bernoulli method here, but i cant seem to get the right answer.

qrious126
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@dan815

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

qrious126
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cool. thanks!

whpalmer4
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Uh, there's a mistake in there, I'm afraid...
\[xy'  y = 2(xy)^{1/2}\]
xy' = 2(xy)^{1/2}+y\]
\[y' = \frac{2(xy)^{1/2}+y}{x} = 2(y/x)^{1/2}\color{red}{+}y/x\]

UnkleRhaukus
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ah yes, thanks for spotting that @whpalmer4

qrious126
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yes, just noticed. thanks!