anonymous
  • anonymous
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?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
\[y'' +4y = 0\] \[y _{1} = \cos(2t)\] \[y _{2} = \sin(2t)\]
amistre64
  • amistre64
how would you know of x=5 is a solution to the equation x+3 = 10 ?
anonymous
  • anonymous
from x+3 =10, i know x =7. that means x=5 is not a solution.

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amistre64
  • amistre64
plug them in and see of they fit ... 5+3 = 10 is not a good fit is it?
anonymous
  • anonymous
correct.
amistre64
  • amistre64
saying 'i know x=7' is not mathical ... in order to prove it you have to show it
anonymous
  • anonymous
oh, so i plug in y1 and the second derivative of y1. and then i do the same for y2.
amistre64
  • amistre64
yes
amistre64
  • amistre64
and doesnt fundamental have to do with wronskians again?
anonymous
  • anonymous
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.
amistre64
  • amistre64
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
anonymous
  • anonymous
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....
amistre64
  • amistre64
i found this ...
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amistre64
  • amistre64
so yeah, plug and play to check that they are solutions, and Wronskian to determine if they are a fun solution set
anonymous
  • anonymous
since the wronskin is not zero they are fundamental...thanks by the way, where did you find that?
amistre64
  • amistre64
http://www.math.cuhk.edu.hk/~wei/odeas4sol.pdf
anonymous
  • anonymous
Thanks.
amistre64
  • amistre64
youre welcome

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