## anonymous 4 years ago how do you solve the initial value problem of 4y(3)+2y=0;y(0)=2y(0)=5y(0)=6

1. anonymous

i got the wrong answer :(

2. anonymous

Can you retype the question? It didn't come out right? What are those 0s? Are they exponents or numbers?

3. anonymous

they are numbers

4. anonymous

But they are 0s?

5. lalaly

What course are studying?

6. anonymous

Here's is the problem again: 4y'''+2y''=0 y(0)=2 y'(0)=5 y''(0)=6

7. anonymous

yes they are zeros

8. anonymous

calc?

9. lalaly

differential eqns:D

10. anonymous

and im taking differential equations

11. anonymous

yes lol

12. anonymous

the 3 in the problem represents the third derivative im sorry the original post looks weird

13. anonymous

its supposed to be 4y'''+2y''=0 as in to the third derivative and the second derivative

14. lalaly

$4r^3+2r^2=0$$2r^2(r+2)=0$$r=0,0,-1/2$so $y=c_1e^{-0.5x}+c_2x+c3$

15. lalaly

$y'=-0.5c_1e^{-0.5x}+c_2$

16. lalaly

$y''=0.25c_1e^{-0.5x}$

17. anonymous

yes i got that but i think i did something wrong after that

18. lalaly

just plug in the values of x and y, nothing'd go wrong

19. anonymous

i did but the answer is wrong! i did y(0)=2=c_1 +c_3

20. anonymous

y'(0)=5=c2-(1/2)c3e^(-1/2x)

21. lalaly

no the e part cancels coz it equals 1 when x =0

22. lalaly

y'(0)=c2-1/2c3

23. anonymous

yea i know and thats how i solved for c2=12

24. lalaly

wait let me do it

25. lalaly

$y(0)=2$$c_1+c_3=2$ $y'(0)=5$$-0.5c_1+c_2=5$ $y''(0)=6$$0.25c_1=6$$c_1=24$ $24+c_3=2$$c_3=-22$$-0.5(24)+c_2=5$$c_2=17$

26. anonymous

I got c2=-7 and thats where i went wrong! thanks soooo much!

27. lalaly

:D:D its ok, its confusing i know lol, ur welcome

28. anonymous

i frogot .5 was negative

29. anonymous

Thanks again! :)

30. lalaly

anytime:)

31. anonymous

32. lalaly

sure:D

33. anonymous

8y''+4y'+4y=0, where y(0)=4 and y'(0)=1

34. lalaly

u want the answers or the whole solution?

35. anonymous

36. anonymous

but if you cant you can give the answer and I can try to work backwards

37. lalaly

ok give me 5 min let me work it out

38. anonymous

thanks sooooo much

39. lalaly

$y=c_1e^{-\frac{x}{4}}\cos(\frac{\sqrt 7}{4}x)+c_2e^{-\frac{x}{4}}\sin(\frac{\sqrt 7}{4}x)$ i got $c_1=4$$c_2=3.02$

40. anonymous

ok let me check thanks again

41. lalaly

:):)

42. anonymous

woohoooo its correct! thanks sooo much

43. lalaly

hehe yaaay :D

44. anonymous

ok i have one last question but if you dont want to do it its totally fine! i had a bunch of roblems to do and these were the three i couldnt get so if its ok can i ask you another one? i feel bad for asking!

45. lalaly

lol dont feel bad, id love to help, why else would i be on openstudy

46. anonymous

true lol thanks soo much! here is the question:

47. anonymous

Find a linear homogeneous constant-coefficient differential equation with the general solution: y(x)=c1e^(2x) + c2Cos(9x) +c3Sin(9x) that has the form y'''+_________y''+_____y'+____y=0 the underscores are supposed to represent blanks lol

48. lalaly

i got off here by mistake :S let me do it again

49. anonymous

okie dokes! :)

50. lalaly

the solutions are 2,+/-9i

51. lalaly

so (r-2)(r^2+81)=0

52. lalaly

r^3-2r^2+81r-162=0

53. lalaly

y'''-2y''+81y'-162y=0

54. anonymous

how did you get the solutions?

55. lalaly

do u know how u find the general solution like when u get r=2,3 the general solution is y=c1e^2x+c_2e^3x and when u get complex solutions a+bi and a-bi the general solution is y=e^ax(c1cos(bx)+c2sin(bx)... u just do it back wards

56. anonymous

oh ok I got it! thnkssss sooo much!!! i really appreciate all yr help!! I also noticed that you joioned 3arabi open stidy group! r u taking arabic classes?

57. anonymous

study*

58. lalaly

lol no im half arab :D:D i speak arabic

59. anonymous

oh lol I was going to ask if you need any help because I also speak arabic and it's my minor

60. lalaly

oh wow really :D:D where are u from hehe

61. anonymous

I'm palestinian! hbu?

62. lalaly

o ana kmaaaaaaaaaaaaaan :D

63. anonymous

but if you're referring to city, I'm from Dearborn lol

64. anonymous

omg nooo waaayyy!!! how cool!

65. lalaly

hehe im from hebron hehe

66. anonymous

oh by dearborn i meant city in the US haha I'm from beit safafa in palestine

67. anonymous

do you live in palestine?

68. lalaly

oh lol i dont know abt US lol, ana 3ayshe bi newzealand

69. anonymous

ooooo keef new zealns? keef al; taqs hunak?

70. anonymous

zealand*

71. lalaly

hehe its summer so yaaaaaaaaay !! :D newzealand btjanen bmoot feha hehe, 3njad sodfe helwee:D:D iza bedik more help ask me :D

72. anonymous

3njad inti bit mooti feeha? lol hon it's winter bes ana behab al pelletaa3! bhab al thalj! and shukran bes khalasit wajabatee! thanks soo much! i really appreciate your help!

73. anonymous

i was supposed to say pelletaa3 not pelletaa3 lol i have no idea hot i typed that instead! lol sorry for the confusion

74. anonymous

pelletaaaa3 as in winter* i dont know why it keeps sending it as something else

75. lalaly

if u catch me on here at anytime ill be glad to help u o sara7a u made my day hehe i was a lil upset, bas u made me smile :D hehe Fhemt-ha

76. anonymous

thanks so much! and same to you! if you have any questions I'll be more than glad to help to the best of my ability! and I'm glad to have made your day! a smile is always better than a frown! :)

77. lalaly

hehe nice to meet you, esme lana btw

78. anonymous

nice to meet you lana! ismee Ranya

79. lalaly

oooo kman my favorite name ya salam hehe

80. anonymous

haha shukran!

81. anonymous

btasif bes lazim arooh leana lazam arooh ijeeb igrath min al mahalat! bye! and talk to you soon inshallah! :)Have a great day!! :)

82. lalaly

:D:D okay take care,, bye byee

83. anonymous

bye :)