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yuki

  • 5 years ago

Differential equations

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  1. anonymous
    • 5 years ago
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    give question......

  2. anonymous
    • 5 years ago
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    wt of them??

  3. Yuki
    • 5 years ago
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    \[y"+3y'-4y = 0\]

  4. Yuki
    • 5 years ago
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    if we let \[y= e^{mx}\]

  5. Yuki
    • 5 years ago
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    I know that we can get \[(m^2 +3m-4)e^{mx}=0\]

  6. anonymous
    • 5 years ago
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    use characteristic equation: m^2+3m-4=0 m=-4 and m=1 so y=c1e^(-4t)+c2e^t

  7. anonymous
    • 5 years ago
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    (d^2+3d-4)y=0 d=4,-1 y=ae^4x+be^-x

  8. Yuki
    • 5 years ago
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    and it factors into \[(m-1)(m+4)=0\]

  9. Yuki
    • 5 years ago
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    so since the roots are real and distinct, y = \[ae^{x}+be^{-4x}\]

  10. anonymous
    • 5 years ago
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    CORRECT

  11. anonymous
    • 5 years ago
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    it will be ae^4x+be^-x.

  12. Yuki
    • 5 years ago
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    but what if \[y"-10y'+25y = 0 \]

  13. anonymous
    • 5 years ago
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    because your char. equation m^2+3m-4=0 has the roots 4,-1.

  14. anonymous
    • 5 years ago
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    (a+bx)e^5x

  15. anonymous
    • 5 years ago
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    Then you have two same roots m=5 and then y=c1te^5t+c2e^5t

  16. Yuki
    • 5 years ago
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    how do we proceed the problem? do we let \[y= xe^{mx}\]

  17. anonymous
    • 5 years ago
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    "because your char. equation m^2+3m-4=0 has the roots 4,-1" dipank this is NOT CORRECT

  18. anonymous
    • 5 years ago
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    yes i checked........sorry for that........

  19. anonymous
    • 5 years ago
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    noproblem, i just didn't want to confuse..

  20. Yuki
    • 5 years ago
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    for the other root I think there was another way to solve it when the roots are equal and real, the formula was different and I think dipank sounds right but I am not sure how to prove it

  21. anonymous
    • 5 years ago
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    long proof..it'd be in your book for sure. circuit theory is the only way i ever wrapped my brain around this concept..a critically damped RLC circuit is modelled by a characteristic equation with two real same roots. Good luck with your proof and further studies though.

  22. dumbcow
    • 5 years ago
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    here is a link that might help you understand repeated roots in characteristic equation http://tutorial.math.lamar.edu/Classes/DE/RepeatedRoots.aspx

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