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anonymous

  • 5 years ago

y''+4y=2sin(2t) y(0)=1 y'(0)=-1solve the I.V.P. the complex root threw me. is it c1cos(2t) +c2sin(2t)?

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  1. myininaya
    • 5 years ago
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    http://www.sosmath.com/tables/diffeq/diffeq.html

  2. myininaya
    • 5 years ago
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    yes you are right so far

  3. anonymous
    • 5 years ago
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    k thanks, i messed up the math somewhere then ill have to redo it.

  4. myininaya
    • 5 years ago
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    that site is nice above

  5. myininaya
    • 5 years ago
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    ok you know we only found the homogeneous solution right?

  6. anonymous
    • 5 years ago
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    yeah i can do the rest i was just unsure about the complex root and setting up the homogeneous solution. i get y(t)=c1(2t) +c2sin(2t)-(1/2)tcos(2t) for the gen solution. that seem right?

  7. myininaya
    • 5 years ago
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    i assume you accidently left out the cos of that constant thingy i will check your solution in just a sec k?

  8. myininaya
    • 5 years ago
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    ok your solution is not checking out i tried it twice maybe a maybe a mistake but let me try actually getting the nonhomogeneous k? thats the only thats not working out right now

  9. myininaya
    • 5 years ago
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    the nonhomogeneous is y=sin(2t)

  10. myininaya
    • 5 years ago
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    wait....lol

  11. myininaya
    • 5 years ago
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    i think thats right its just weird to see the nonhomogeneous solution as a part of the homogenous solution

  12. myininaya
    • 5 years ago
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    let me see what i come up with doing what you which i think you tried y=Atcos(2t) right?

  13. myininaya
    • 5 years ago
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    i think i made a mistake in checking it because your solution is what i just found sorry

  14. myininaya
    • 5 years ago
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    did you try checking it?

  15. anonymous
    • 5 years ago
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    haha yes. i think its all set i went back over the work. man i miss diff eq. that class was interesting.

  16. myininaya
    • 5 years ago
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    lol

  17. anonymous
    • 5 years ago
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    Refer to the attachment.

  18. myininaya
    • 5 years ago
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    i'm confused why are you doing t's and x's?

  19. anonymous
    • 5 years ago
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    Well is my face red. Mortified. The second solution version is attached. Everything is in terms of the independent variable t now.

  20. anonymous
    • 5 years ago
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    Some of the more complex expressions could be further simplified.

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