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anonymous

  • one year ago

How can I verify that the functions y1 and y2 are solutions of the differential equation? And how do I know if they constitute a fundamental set of solutions?

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  1. anonymous
    • one year ago
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    \[y'' +4y = 0\] \[y _{1} = \cos(2t)\] \[y _{2} = \sin(2t)\]

  2. amistre64
    • one year ago
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    how would you know of x=5 is a solution to the equation x+3 = 10 ?

  3. anonymous
    • one year ago
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    from x+3 =10, i know x =7. that means x=5 is not a solution.

  4. amistre64
    • one year ago
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    plug them in and see of they fit ... 5+3 = 10 is not a good fit is it?

  5. anonymous
    • one year ago
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    correct.

  6. amistre64
    • one year ago
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    saying 'i know x=7' is not mathical ... in order to prove it you have to show it

  7. anonymous
    • one year ago
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    oh, so i plug in y1 and the second derivative of y1. and then i do the same for y2.

  8. amistre64
    • one year ago
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    yes

  9. amistre64
    • one year ago
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    and doesnt fundamental have to do with wronskians again?

  10. anonymous
    • one year ago
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    correct. that means i will have to take the wronskian of y1 and y2 and verify that the determinant of their matrix is not equal to zero.

  11. amistre64
    • one year ago
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    is that the only property of a fundamental solution set that we need to satisfy? im not familiar with the properties so i wouldnt know what else to check

  12. anonymous
    • one year ago
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    Well, I am taking Diff EQ and for now, this is the only method we learned. We're only 10 lectures into class.... that is only Chapter 3 in the book. As far as my knowledge goes, that's the only way i can prove this...for now....

  13. amistre64
    • one year ago
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    i found this ...

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  14. amistre64
    • one year ago
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    so yeah, plug and play to check that they are solutions, and Wronskian to determine if they are a fun solution set

  15. anonymous
    • one year ago
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    since the wronskin is not zero they are fundamental...thanks by the way, where did you find that?

  16. amistre64
    • one year ago
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    http://www.math.cuhk.edu.hk/~wei/odeas4sol.pdf

  17. anonymous
    • one year ago
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    Thanks.

  18. amistre64
    • one year ago
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    youre welcome

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