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roadjester Group Title

How the heck do I solve this diff. eq?

  • one year ago
  • one year ago

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  1. roadjester Group Title
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    \[\large ({{y \over x} + e^{-xy}})dx + dy =0\]

    • one year ago
  2. oldrin.bataku Group Title
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    First, multiply through by \(xe^{xy}\):$$(ye^{xy}+x)dx+xe^{xy}dy=0$$Do you know how to solve from here?

    • one year ago
  3. roadjester Group Title
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    It doesn't look seperable, I still have y in the exponent of the dx term

    • one year ago
  4. oldrin.bataku Group Title
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    If only there were some function \(f\) s.t. \(\frac{\partial f}{\partial x}=ye^{xy}+x\), \(\frac{\partial f}{\partial y}=xe^{xy}\)... (I didn't solve it using separation of variables)

    • one year ago
  5. roadjester Group Title
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    you did partial differentiation...but I'm not quite sure of what

    • one year ago
  6. oldrin.bataku Group Title
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    Have you studied exact differential equations yet? If we integrate both sides of our original equation, assuming that there is some function \(f\) whose partial derivatives match whatever we've multiplied by \(dx\), \(dy\) respectively, we end up with \(f(x,y)=c\)... now, we merely need to determine what \(f\) is!

    • one year ago
  7. roadjester Group Title
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    not yet

    • one year ago
  8. roadjester Group Title
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    only homogenous diff. eq, and substitution

    • one year ago
  9. oldrin.bataku Group Title
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    Well, we know it's not homogeneous:$$(\frac{y}x+e^{-xy})dx+dy=0\\\frac{dy}{dx}=-[\frac{y}x+e^{-xy}]\\$$

    • one year ago
  10. roadjester Group Title
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    I get how you got that...but how does writing it as dy/dx help?

    • one year ago
  11. oldrin.bataku Group Title
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    It's to show how it's not homogeneous.

    • one year ago
  12. roadjester Group Title
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    how can you tell it's not homogeneous?

    • one year ago
  13. roadjester Group Title
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    \[\large y(1)=0\]

    • one year ago
  14. oldrin.bataku Group Title
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    Does \(\frac{ty}{tx}+e^{-(tx)(ty)}=\frac{y}x+e^{-xy}\)?

    • one year ago
  15. roadjester Group Title
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    I don't know? That was an Intial condition that I forgot to type...

    • one year ago
  16. oldrin.bataku Group Title
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    Do you know how to test whether an ODE is homogeneous?

    • one year ago
  17. roadjester Group Title
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    ODE? I'm guesing DE is diff. eq.

    • one year ago
  18. oldrin.bataku Group Title
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    ordinary differential equation

    • one year ago
  19. roadjester Group Title
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    no clue

    • one year ago
  20. oldrin.bataku Group Title
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    So you haven't learned about homogeneous differential equations?

    • one year ago
  21. roadjester Group Title
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    homogeneous yes, ordinary, not a term we've used

    • one year ago
  22. oldrin.bataku Group Title
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    Ordinary is on contrast with partial differential equations, where you have partial derivatives.

    • one year ago
  23. roadjester Group Title
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    you realize that I'm totally confused right? this is only my second class meeting

    • one year ago
  24. oldrin.bataku Group Title
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    :-p ok well tell me what you've been taught so far.

    • one year ago
  25. roadjester Group Title
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    just separating the terms and substitution if the equation can't be solved on the spot

    • one year ago
  26. oldrin.bataku Group Title
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    I don't think it can be solved using either technique. Maybe you need to learn how to solve exact equations first.

    • one year ago
  27. ljensen Group Title
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    Use the substitution \(u(x)=xy(x).\) Then \(u^\prime=xy^\prime+y\). This results in an easy equation for \(u(x).\)

    • one year ago
  28. robtobey Group Title
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    Hope this helps.

    • one year ago
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  29. oldrin.bataku Group Title
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    ... are you seriously just posting links to what Mathematica or Wolfram|Alpha spits out?

    • one year ago
  30. robtobey Group Title
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    Yes.

    • one year ago
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is replying to Can someone tell me what button the professor is hitting...

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