## 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?

1. anonymous

$y'' +4y = 0$ $y _{1} = \cos(2t)$ $y _{2} = \sin(2t)$

2. amistre64

how would you know of x=5 is a solution to the equation x+3 = 10 ?

3. anonymous

from x+3 =10, i know x =7. that means x=5 is not a solution.

4. amistre64

plug them in and see of they fit ... 5+3 = 10 is not a good fit is it?

5. anonymous

correct.

6. amistre64

saying 'i know x=7' is not mathical ... in order to prove it you have to show it

7. anonymous

oh, so i plug in y1 and the second derivative of y1. and then i do the same for y2.

8. amistre64

yes

9. amistre64

and doesnt fundamental have to do with wronskians again?

10. 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.

11. 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

12. 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....

13. amistre64

i found this ...

14. amistre64

so yeah, plug and play to check that they are solutions, and Wronskian to determine if they are a fun solution set

15. anonymous

since the wronskin is not zero they are fundamental...thanks by the way, where did you find that?

16. amistre64
17. anonymous

Thanks.

18. amistre64

youre welcome