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anonymous

  • 5 years ago

method of undetermined coefficients 4y''+8y'+13y=1, y(0)=0, y'(0)=1/13

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  1. anonymous
    • 5 years ago
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    use the quadratic formula find the roots to the characteristic polynomial \[4s ^{2}+8s+13=0\] then find all the solns to the corresponding homogenous D E . find a particular solution to the DE and put them together

  2. anonymous
    • 5 years ago
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    i got to the point \[\left( -8\pm \sqrt{-144} \right)\div8\] bit confused with the negative square root

  3. anonymous
    • 5 years ago
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    do i have to get imaginary numbers involved?

  4. anonymous
    • 5 years ago
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    \[\sqrt{-144}= 12i\]

  5. anonymous
    • 5 years ago
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    \[y _{p}=1/13\] is a particular soln to the DE

  6. anonymous
    • 5 years ago
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    the homo soln will be \[y _{h}(t)= c _{1}e ^{t}\cos8/12t+c _{2}e ^{t} \sin8/12\]

  7. anonymous
    • 5 years ago
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    add the part. soln to this, then use your init values to solve for \[c _{1}, c _{2}\]

  8. anonymous
    • 5 years ago
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    when u put 8/12 do you mean 12/8?

  9. anonymous
    • 5 years ago
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    yes sorry

  10. anonymous
    • 5 years ago
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    and can you put it in brackets please?

  11. anonymous
    • 5 years ago
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    actually, i get that now, dont worry bout brackets

  12. anonymous
    • 5 years ago
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    what do you mean

  13. anonymous
    • 5 years ago
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    ok

  14. anonymous
    • 5 years ago
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    thanks for all the help, i have the final answer as \[y(x)=\exp(x)[(2/39)\sin ((3/2)x)]+(1/13)\] do you know if that is right?

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