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anonymous

  • 5 years ago

Find the unique solution to the differential equation yʹʹ−11yʹ+30y=−60t^(2)+104t−56 satisfying the initial conditions y(0)=6 and yʹ(0)=41 Answer: y(t)= Your answer should be a function of t.

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  1. anonymous
    • 5 years ago
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    I mostly don't understand how to get the right hand side of the equation. So far I've only done these when the right side was 0

  2. myininaya
    • 5 years ago
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    don't you choose y=at^2+bt+c and don't forget to add your homogenous solutions

  3. anonymous
    • 5 years ago
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    c1 e^(5 t)+c2 e^(6 t)-2 t^2+2 t-1 Does that seem right?

  4. myininaya
    • 5 years ago
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    so far i got a=-2 let be check your b and c

  5. myininaya
    • 5 years ago
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    i got a different coefficient for t

  6. myininaya
    • 5 years ago
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    i got 21/5

  7. anonymous
    • 5 years ago
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    so you got c1 e^(5 t)+c2 e^(6 t)-2 t^2+(21/5)t-1 ?

  8. anonymous
    • 5 years ago
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    I got y[t] = -1 + 3 E^(5 t) + 4 E^(6 t) + 2 t - 2 t^2

  9. anonymous
    • 5 years ago
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    Yeah I got that too, I'll see if it's right

  10. anonymous
    • 5 years ago
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    It is, I've checked with a DSolve software.

  11. anonymous
    • 5 years ago
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    Okay great thanks a lot

  12. anonymous
    • 5 years ago
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    no problem!

  13. anonymous
    • 5 years ago
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    I'm new to this, do I press something to rate you or something?

  14. anonymous
    • 5 years ago
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    I'm not sure, I'm new too. probably clicking become a fan does the trick.

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spraguer (Moderator)
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