Use the substitution of x=e^{t} to transform the given cauchy-euler differential equation to a differential equation with constant coefficients then solve that by any method. (finding the characterristic (auxiliary) equation or variation of parameters). do not forget to re-subtitute for x after you solve the equation.
x^{2}y^{''}+9xy^{'}-20y=0

By the chain rule,

which follows from .

is then a function of ; denote this function by . Then by the product rule,

and by the chain rule,

so that

Then the ODE in terms of is

The characteristic equation

has two roots at and , so the characteristic solution is

Solving in terms of gives

answer: b.

step-by-step explanation:

the y coordinate for point b is 0, and answer b is the only one with that y coordinate.

1. 3.4/4

2. 0.8/7

3. 0.5 x 3

4. 0.9 x 6

5. 10.8

6. 2.35

7. 0.567

8. 9.35

9. 0.02

10. 0.06

11. 0.16

12. 0.42

13. 0.63

14. 5.6

15. 8.1

16. 9.9

17. 0.28

18. 0.48

19. 0.27

20. 0.49

21. 0.45

22. 0.72

23. 0.9

24. 0.88

25. 0.75

26. 0.16

27. 0.328

28. 0.495

29. 0.72

30. 1.068