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qrious126

  • 2 years ago

How would you go about solving this equation?

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  1. qrious126
    • 2 years ago
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    \[xy \prime - y = 2(xy)^{1/2}\]

  2. qrious126
    • 2 years ago
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    @UnkleRhaukus

  3. qrious126
    • 2 years ago
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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.

  4. qrious126
    • 2 years ago
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    @dan815

  5. UnkleRhaukus
    • 2 years ago
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    \[xy^\prime - y = 2(xy)^{1/2}\\y'=\frac{2(xy)^{1/2}-y}x\\=2(y/x)^{1/2}-y/x\]

  6. qrious126
    • 2 years ago
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    cool. thanks!

  7. whpalmer4
    • 2 years ago
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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\] \[y' = \frac{2(xy)^{1/2}+y}{x} = 2(y/x)^{1/2}\color{red}{+}y/x\]

  8. UnkleRhaukus
    • 2 years ago
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    ah yes, thanks for spotting that @whpalmer4

  9. qrious126
    • 2 years ago
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    yes, just noticed. thanks!

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