Question

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

Answer 1

i got the wrong answer :(

Answer 2

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

Answer 3

they are numbers

Answer 4

But they are 0s?

Answer 5

What course are studying?

Answer 6

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

Answer 7

yes they are zeros

Answer 8

calc?

Answer 9

differential eqns:D

Answer 10

and im taking differential equations

Answer 11

yes lol

Answer 12

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

Answer 13

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

Answer 14

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

Answer 15

\[y'=-0.5c_1e^{-0.5x}+c_2\]

Answer 16

\[y''=0.25c_1e^{-0.5x}\]

Answer 17

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

Answer 18

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

Answer 19

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

Answer 20

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

Answer 21

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

Answer 22

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

Answer 23

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

Answer 24

wait let me do it

Answer 25

\[y(0)=2\]\[c_1+c_3=2\]

\[y'(0)=5\]\[-0.5c_1+c_2=5\]

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

Answer 26

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

Answer 27

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

Answer 28

i frogot .5 was negative

Answer 29

Thanks again! :)

Answer 30

anytime:)

Answer 31

can I ask another question?

Answer 32

sure:D

Answer 33

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

Answer 34

u want the answers or the whole solution?

Answer 35

the solution please

Answer 36

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

Answer 37

ok give me 5 min let me work it out

Answer 38

thanks sooooo much

Answer 39

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

Answer 40

ok let me check thanks again

Answer 41

:):)

Answer 42

woohoooo its correct! thanks sooo much

Answer 43

hehe yaaay :D

Answer 44

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!

Answer 45

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

Answer 46

true lol thanks soo much! here is the question:

Answer 47

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

Answer 48

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

Answer 49

okie dokes! :)

Answer 50

the solutions are
2,+/-9i

Answer 51

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

Answer 52

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

Answer 53

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

Answer 54

how did you get the solutions?

Answer 55

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

Answer 56

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?

Answer 57

study*

Answer 58

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

Answer 59

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

Answer 60

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

Answer 61

I'm palestinian! hbu?

Answer 62

o ana kmaaaaaaaaaaaaaan :D

Answer 63

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

Answer 64

omg nooo waaayyy!!! how cool!

Answer 65

hehe im from hebron hehe

Answer 66

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

Answer 67

do you live in palestine?

Answer 68

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

Answer 69

ooooo keef new zealns? keef al; taqs hunak?

Answer 70

zealand*

Answer 71

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

Answer 72

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!

Answer 73

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

Answer 74

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

Answer 75

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

Answer 76

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! :)

Answer 77

hehe nice to meet you, esme lana btw

Answer 78

nice to meet you lana! ismee Ranya

Answer 79

oooo kman my favorite name ya salam hehe

Answer 80

haha shukran!

Answer 81

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

Answer 82

:D:D okay take care,, bye byee

Answer 83

bye :)