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haganmc Group Title

how to solve this diff equation?? dx/dt−x^3=x

  • 2 years ago
  • 2 years ago

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  1. lgbasallote Group Title
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    have you tried Bernoulli's?

    • 2 years ago
  2. Algebraic! Group Title
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    dx/dt = x+x^3 divide by x+x^3 multiply by dt

    • 2 years ago
  3. haganmc Group Title
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    the final answer should be \[x=\pm \sqrt{C ^{2t}/(1-Ce ^{2t})}\]

    • 2 years ago
  4. ironmanjimbo Group Title
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    Multiplying by dt is impossible! Rates of change are as is.

    • 2 years ago
  5. Algebraic! Group Title
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    lol

    • 2 years ago
  6. haganmc Group Title
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    you get \[\frac{ 1 }{ x+x^3 }dx=dt\]

    • 2 years ago
  7. haganmc Group Title
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    but how do you integrate this??

    • 2 years ago
  8. ironmanjimbo Group Title
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    haganmc is right on, what he did is separation of variables which is not the same as multiplying by a component of a rate of change. Well done. Now go with factoring and partial fraction decomposition and you are on your way to a solution

    • 2 years ago
  9. Algebraic! Group Title
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    @haganmc ... looks good to me.

    • 2 years ago
  10. Algebraic! Group Title
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    oh that wasn't your answer?

    • 2 years ago
  11. Algebraic! Group Title
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    book's answer?

    • 2 years ago
  12. haganmc Group Title
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    no now You have to integrate both sides.. i am trying to get x by itself

    • 2 years ago
  13. haganmc Group Title
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    but how do you do partial fraction decomposition?

    • 2 years ago
  14. Algebraic! Group Title
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    use partial frac. expansion on 1/(x+x^3)

    • 2 years ago
  15. Algebraic! Group Title
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    A / x + Bx /(x^2+1)

    • 2 years ago
  16. haganmc Group Title
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    thats where i messed up... i didnt put an x after the B

    • 2 years ago
  17. ironmanjimbo Group Title
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    Algebraic, YES, nice going!

    • 2 years ago
  18. Algebraic! Group Title
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    _Multiplying by dt is impossible! Rates of change are as is._

    • 2 years ago
  19. ironmanjimbo Group Title
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    That is correct. What you are actually doing is separation of variables, It is an important distinction!!!

    • 2 years ago
  20. Algebraic! Group Title
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    go learn the chain rule

    • 2 years ago
  21. ironmanjimbo Group Title
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    I don't mind if you do not want to agree with me, but I will simply suggest that you look into what I'm pointing out regarding how the rate of change is separated in such equations. Simply put, it LOOKS like dt was multiplied, but it was not.

    • 2 years ago
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