anonymous
  • anonymous
how do you solve the initial value problem of 4y(3)+2y=0;y(0)=2y(0)=5y(0)=6
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
i got the wrong answer :(
anonymous
  • anonymous
Can you retype the question? It didn't come out right? What are those 0s? Are they exponents or numbers?
anonymous
  • anonymous
they are numbers

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anonymous
  • anonymous
But they are 0s?
lalaly
  • lalaly
What course are studying?
anonymous
  • anonymous
Here's is the problem again: 4y'''+2y''=0 y(0)=2 y'(0)=5 y''(0)=6
anonymous
  • anonymous
yes they are zeros
anonymous
  • anonymous
calc?
lalaly
  • lalaly
differential eqns:D
anonymous
  • anonymous
and im taking differential equations
anonymous
  • anonymous
yes lol
anonymous
  • anonymous
the 3 in the problem represents the third derivative im sorry the original post looks weird
anonymous
  • anonymous
its supposed to be 4y'''+2y''=0 as in to the third derivative and the second derivative
lalaly
  • lalaly
\[4r^3+2r^2=0\]\[2r^2(r+2)=0\]\[r=0,0,-1/2\]so \[y=c_1e^{-0.5x}+c_2x+c3\]
lalaly
  • lalaly
\[y'=-0.5c_1e^{-0.5x}+c_2\]
lalaly
  • lalaly
\[y''=0.25c_1e^{-0.5x}\]
anonymous
  • anonymous
yes i got that but i think i did something wrong after that
lalaly
  • lalaly
just plug in the values of x and y, nothing'd go wrong
anonymous
  • anonymous
i did but the answer is wrong! i did y(0)=2=c_1 +c_3
anonymous
  • anonymous
y'(0)=5=c2-(1/2)c3e^(-1/2x)
lalaly
  • lalaly
no the e part cancels coz it equals 1 when x =0
lalaly
  • lalaly
y'(0)=c2-1/2c3
anonymous
  • anonymous
yea i know and thats how i solved for c2=12
lalaly
  • lalaly
wait let me do it
lalaly
  • lalaly
\[y(0)=2\]\[c_1+c_3=2\] \[y'(0)=5\]\[-0.5c_1+c_2=5\] \[y''(0)=6\]\[0.25c_1=6\]\[c_1=24\] \[24+c_3=2\]\[c_3=-22\]\[-0.5(24)+c_2=5\]\[c_2=17\]
anonymous
  • anonymous
I got c2=-7 and thats where i went wrong! thanks soooo much!
lalaly
  • lalaly
:D:D its ok, its confusing i know lol, ur welcome
anonymous
  • anonymous
i frogot .5 was negative
anonymous
  • anonymous
Thanks again! :)
lalaly
  • lalaly
anytime:)
anonymous
  • anonymous
can I ask another question?
lalaly
  • lalaly
sure:D
anonymous
  • anonymous
8y''+4y'+4y=0, where y(0)=4 and y'(0)=1
lalaly
  • lalaly
u want the answers or the whole solution?
anonymous
  • anonymous
the solution please
anonymous
  • anonymous
but if you cant you can give the answer and I can try to work backwards
lalaly
  • lalaly
ok give me 5 min let me work it out
anonymous
  • anonymous
thanks sooooo much
lalaly
  • 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 \[c_1=4\]\[c_2=3.02\]
anonymous
  • anonymous
ok let me check thanks again
lalaly
  • lalaly
:):)
anonymous
  • anonymous
woohoooo its correct! thanks sooo much
lalaly
  • lalaly
hehe yaaay :D
anonymous
  • 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!
lalaly
  • lalaly
lol dont feel bad, id love to help, why else would i be on openstudy
anonymous
  • anonymous
true lol thanks soo much! here is the question:
anonymous
  • 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
lalaly
  • lalaly
i got off here by mistake :S let me do it again
anonymous
  • anonymous
okie dokes! :)
lalaly
  • lalaly
the solutions are 2,+/-9i
lalaly
  • lalaly
so (r-2)(r^2+81)=0
lalaly
  • lalaly
r^3-2r^2+81r-162=0
lalaly
  • lalaly
y'''-2y''+81y'-162y=0
anonymous
  • anonymous
how did you get the solutions?
lalaly
  • 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
anonymous
  • 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?
anonymous
  • anonymous
study*
lalaly
  • lalaly
lol no im half arab :D:D i speak arabic
anonymous
  • anonymous
oh lol I was going to ask if you need any help because I also speak arabic and it's my minor
lalaly
  • lalaly
oh wow really :D:D where are u from hehe
anonymous
  • anonymous
I'm palestinian! hbu?
lalaly
  • lalaly
o ana kmaaaaaaaaaaaaaan :D
anonymous
  • anonymous
but if you're referring to city, I'm from Dearborn lol
anonymous
  • anonymous
omg nooo waaayyy!!! how cool!
lalaly
  • lalaly
hehe im from hebron hehe
anonymous
  • anonymous
oh by dearborn i meant city in the US haha I'm from beit safafa in palestine
anonymous
  • anonymous
do you live in palestine?
lalaly
  • lalaly
oh lol i dont know abt US lol, ana 3ayshe bi newzealand
anonymous
  • anonymous
ooooo keef new zealns? keef al; taqs hunak?
anonymous
  • anonymous
zealand*
lalaly
  • lalaly
hehe its summer so yaaaaaaaaay !! :D newzealand btjanen bmoot feha hehe, 3njad sodfe helwee:D:D iza bedik more help ask me :D
anonymous
  • 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!
anonymous
  • anonymous
i was supposed to say pelletaa3 not pelletaa3 lol i have no idea hot i typed that instead! lol sorry for the confusion
anonymous
  • anonymous
pelletaaaa3 as in winter* i dont know why it keeps sending it as something else
lalaly
  • 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
anonymous
  • 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! :)
lalaly
  • lalaly
hehe nice to meet you, esme lana btw
anonymous
  • anonymous
nice to meet you lana! ismee Ranya
lalaly
  • lalaly
oooo kman my favorite name ya salam hehe
anonymous
  • anonymous
haha shukran!
anonymous
  • anonymous
btasif bes lazim arooh leana lazam arooh ijeeb igrath min al mahalat! bye! and talk to you soon inshallah! :)Have a great day!! :)
lalaly
  • lalaly
:D:D okay take care,, bye byee
anonymous
  • anonymous
bye :)

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