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lilMissMindset

  • 3 years ago

one more help please. some difficult DEs which I can't figure out. dx + (y^2x)dy = (x^2 y) dy

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  1. lilMissMindset
    • 3 years ago
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    it is : dx + (y^2 *x)dy = (x^2 *y) dy

  2. amistre64
    • 3 years ago
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    i wonder: \[\frac{dx}{dy}+xy^2=x^2y\] \[x^{-2}x'+y^2x^{-1}=y\] \[z=x^{-1}:~z^{-1}=x;~z^{2}=x^{-2};~-z^{-2}z'=x';~\] \[z^2(-z^{-2}z')+y^2z=y\] \[-z'+y^2z=y\] \[z'-y^2z=-y\] justwondering, i got no idea if its right tho

  3. amistre64
    • 3 years ago
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    \[e^{-\frac{1}{3}y^3}z'-y^2e^{-\frac{1}{3}y^3}z=-ye^{-\frac{1}{3}y^3}\] \[e^{-\frac{1}{3}y^3}z=-\int ye^{-\frac{1}{3}y^3}dy\] \[z=-~e^{\frac{1}{3}y^3}\int ye^{-\frac{1}{3}y^3}dy\]

  4. amistre64
    • 3 years ago
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    i doubt that was right; unless we were spose to go into the Gamma function :/

  5. amistre64
    • 3 years ago
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    any ideas on how to start lilMiss ??

  6. lilMissMindset
    • 3 years ago
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    sorry. poor internet connection here. well, what i was thinking was to get the integrating factor of the equation.

  7. lilMissMindset
    • 3 years ago
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    just the same as what you did, i guess?

  8. amistre64
    • 3 years ago
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    the twp dys have me iffy; i have never had to deal with them in that state

  9. amistre64
    • 3 years ago
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    dx + (y^2x)dy = (x^2 y) dy dx = (x^2y - y^2x)dy dx/dy = x^2y - y^2x

  10. amistre64
    • 3 years ago
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    http://www.wolframalpha.com/input/?i=dx%2Fdy+%3D+x%5E2y+-+y%5E2x i run into a gamma function at every turn :/

  11. lilMissMindset
    • 3 years ago
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    help! integrate this please. : int. e^(-1/3 *y^3)dy

  12. mukushla
    • 3 years ago
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    i think there is no closed form for that integral ---------------------------------------------------------------------- \[M\text{d}x+N\text{d}y=0\]another method is multiplynig by \(x^a.y^b\) and searching for \(a\) and \(b\) for which\[\frac{\partial (x^a.y^b.M)}{\partial y}=\frac{\partial (x^a.y^b.N)}{\partial x}\]which turnes the equation to an exact diff equation let me try it

  13. mukushla
    • 3 years ago
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    no its not working im wondering where these equations come from...this one and prev are very curious...

  14. lilMissMindset
    • 3 years ago
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    i already got this one, using bernoulli's equation with respect to x, are you familiar wit that? my only problem is how am i going to integrate e^(-1/3 *y^3)dy

  15. mukushla
    • 3 years ago
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    \[\large \int e^{-\frac{y^3}{3}} dy\]?

  16. mukushla
    • 3 years ago
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    but there is no closed form for this integral...

  17. lilMissMindset
    • 3 years ago
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    why? i'll try it in wolfram alpha

  18. mukushla
    • 3 years ago
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    http://www.wolframalpha.com/input/?i=integrate++e%5E%28-x%5E3%29

  19. lilMissMindset
    • 3 years ago
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    :(

  20. lilMissMindset
    • 3 years ago
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    will i pass my midterm? :(

  21. mukushla
    • 3 years ago
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    sure u will...dont think of these 2 prev problems

  22. mukushla
    • 3 years ago
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    they were not normal

  23. lilMissMindset
    • 3 years ago
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    aw. thank you so much. really really thank you for everything that you've done just so i could have answers. one medal isn't enough, i guess. :)

  24. mukushla
    • 3 years ago
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    welcome...:)

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