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anonymous

  • one year ago

Can someone help a novice out?! Differential Equation SOS! Find the DE knowing the final answer y=(x-c)^3 Thanks a lot!!!

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  1. anonymous
    • one year ago
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    Should I just get rid of the C?

  2. anonymous
    • one year ago
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    and if so. idk really know how tbh

  3. anonymous
    • one year ago
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    @ganeshie8

  4. anonymous
    • one year ago
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    @idku

  5. anonymous
    • one year ago
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    but the C remains! shouldn't I come to the point of which I don't have constants?

  6. anonymous
    • one year ago
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    hahahahahah

  7. anonymous
    • one year ago
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    well thanks anyhow

  8. anonymous
    • one year ago
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    @arthurpariz

  9. anonymous
    • one year ago
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    @Loser66 will you be my savior?

  10. anonymous
    • one year ago
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    thanks a lot!!!!

  11. freckles
    • one year ago
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    You can find y' by differentiating the y=(x-c)^3.

  12. freckles
    • one year ago
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    why can't the differential equation be y'=3(x-c)^2 with condition .. let me figure it out... y=(x-c)^3+C y(0)=(0-c)^3+C y(0)=-c^3+C y(0)+c^3=C So why can't the differential equation be y'=3(x-c)^2 with condition y(0)=-c^3 ?

  13. mathmate
    • one year ago
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    y=(x-c)^3 y'=3(y-c)^2 y"=6(y-c) so y=(y"/6)^3 or (y")^3-216y=0

  14. mathmate
    • one year ago
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    oh, sorry, I didn't see the condition.

  15. freckles
    • one year ago
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    I don't see how these rules in which we find a differential equation posted in the original post. @Loser66

  16. freckles
    • one year ago
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    I don't see that we aren't allowed to use initial conditions or find a non-linear diff equation.

  17. freckles
    • one year ago
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    it would be nice though if @Hipocampus can settle what we are talking about though

  18. anonymous
    • one year ago
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    hmmm that's all I have...

  19. anonymous
    • one year ago
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    @freckles

  20. anonymous
    • one year ago
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    idk more than you guys about this question

  21. freckles
    • one year ago
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    So the solution can be non-linear or can have conditions ?

  22. anonymous
    • one year ago
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    I believe so

  23. anonymous
    • one year ago
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    as long as the C is gone

  24. Loser66
    • one year ago
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    @freckles You see, @mathmate derives to another way, we have another ODE. I have a bunch of ODE satisfy the given information. YOu add more condition to get another one. That is the reason why it is invalid!! We know that the solution of ODE is UNIQUE for a specific condition. Unfortunately, we didn't have it.

  25. anonymous
    • one year ago
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    thanks a lot guys!

  26. anonymous
    • one year ago
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    can I ask another question then?

  27. Loser66
    • one year ago
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    close this and open a new one, please.

  28. anonymous
    • one year ago
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    Roger @Loser66 !

  29. Loser66
    • one year ago
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    @ganeshie8 @dan815 @oldrin.bataku @SithsAndGiggles @Hipocampus That is the reason why I don't want you to mix this question with the other one

  30. freckles
    • one year ago
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    Oh so no conditions allowed you are saying @Loser66

  31. Loser66
    • one year ago
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    @freckles I didn't say "no conditions allowed", just don't use the un-given conditions.

  32. freckles
    • one year ago
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    you want to find a differential equation subject to no conditions is what you are looking for the rest are valid though if you provide conditions in which I have

  33. freckles
    • one year ago
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    you get to make up the differential equation, why can't you make up the conditions that it is subject to?

  34. freckles
    • one year ago
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    and I'm not really making it up I'm based my condition off what the solution should be.

  35. Loser66
    • one year ago
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    Anyway!! I think if we make up a condition and have a Unique solution for that condition, we are ok :)

  36. Loser66
    • one year ago
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    I am with you now :)

  37. ganeshie8
    • one year ago
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    aren't we looking for the differential equation of order 1, whose general solution is the set of standard cubics translated horizontally ?

  38. freckles
    • one year ago
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    I don't know it wasn't specify that had to have order 1

  39. ganeshie8
    • one year ago
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    the order has to be 1 because there is only 1 arbitrary constant in the given general solution

  40. ganeshie8
    • one year ago
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    number of arbitrary constants and the order of de must agree, right

  41. freckles
    • one year ago
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    well I was thinking that this would be okay: \[y'=3(x-c)^2 \text{ with condition } y(0)=-c^3 \] but are you saying we are suppose to be treating the c from y=(x-c)^3 has like the constant of integration

  42. freckles
    • one year ago
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    meant to end that with a ?

  43. ganeshie8
    • one year ago
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    this should work \[(y')^3 = 27y^2\]

  44. freckles
    • one year ago
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    I like that requires no conditions

  45. freckles
    • one year ago
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    but I still think my way is valid

  46. freckles
    • one year ago
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    only because there was not much put into the "rules" of finding the differential equation

  47. ganeshie8
    • one year ago
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    Haha true, they should have asked it less ambiguously: eliminate the arbitrary constant to get the differential equation that represents the family of standard cubics translated horizontally

  48. anonymous
    • one year ago
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    you could just do: $$y=(x-c)^3\\y^{1/3}=x-c\\\frac13 y^{2/3}y'=1\\y'=3y^{-2/3}$$

  49. anonymous
    • one year ago
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    the solutions are the one-parameter family of monic cubics up to horizontal translation \(y=(x-c)^3\)

  50. anonymous
    • one year ago
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    oops, that should read \(\frac13 y^{-2/3}y'=1\implies y'=3y^{2/3}\) but same point

  51. anonymous
    • one year ago
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    thanks a lot!

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