Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
ranyai12
Group Title
Help Please!!
Use Laplace transforms to solve the initial value problem
x''+4x'+8x=2e^(t) ; x(0)=0 and x'(0)=4
 2 years ago
 2 years ago
ranyai12 Group Title
Help Please!! Use Laplace transforms to solve the initial value problem x''+4x'+8x=2e^(t) ; x(0)=0 and x'(0)=4
 2 years ago
 2 years ago

This Question is Closed

ranyai12 Group TitleBest ResponseYou've already chosen the best response.0
@TuringTest
 2 years ago

ranyai12 Group TitleBest ResponseYou've already chosen the best response.0
this is what I got so far
 2 years ago

ranyai12 Group TitleBest ResponseYou've already chosen the best response.0
after this I am stuck :(
 2 years ago

ranyai12 Group TitleBest ResponseYou've already chosen the best response.0
and this is the table I used: http://tutorial.math.lamar.edu/pdf/Laplace_Table.pdf
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
use partial fractions on the \[\frac2{s(s+1)(s+4)}\]part and I think it should be pretty straightforward to do inverse Laplace
 2 years ago

ranyai12 Group TitleBest ResponseYou've already chosen the best response.0
but what I do about the 4/s^2+4s
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
factor out the s and that is what I wrote
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
oh I see; same thing though factor out s and do partial fractions
 2 years ago

ranyai12 Group TitleBest ResponseYou've already chosen the best response.0
but then you get 4/(s(s+4)>4/s[1/s+4)> 4e^(4t)
 2 years ago

ranyai12 Group TitleBest ResponseYou've already chosen the best response.0
is that right?
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
\[\frac4{s^2+4s}=\frac As+\frac B{s+4}\implies A(s+4)+Bs=4\]\[A=1~~~,B=1\]
 2 years ago

ranyai12 Group TitleBest ResponseYou've already chosen the best response.0
oh so you do partial fractions with both of them
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
that's what I'd do, yeah
 2 years ago

ranyai12 Group TitleBest ResponseYou've already chosen the best response.0
and for the other one it's A(s^2+4s) B(s+1) right
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
\[\mathcal L^{1}\{\frac1s\}=1\]\[\mathcal L^{1}\{\frac1{s+4}\}=e^{4t}\]
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
for the other one it would be...
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
\[\frac2{s(s+1)(s+4)}=\frac As+\frac B{s+1}+\frac C{s+4}\]
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
\[A(s+1)(s+4)+Bs(s+4)+Cs(s+1)=2\]
 2 years ago

ranyai12 Group TitleBest ResponseYou've already chosen the best response.0
then you get As^2+5As+4A+Bs^2+4Bs+Cs^2+C=2
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
not necessary I don't think plug in s=1,4,and 0 and I think you can get the values quickly
 2 years ago

ranyai12 Group TitleBest ResponseYou've already chosen the best response.0
so you dont need ti distribute it?
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
not necessarily how did I get the other answers? I'll show you...
 2 years ago

ranyai12 Group TitleBest ResponseYou've already chosen the best response.0
i didnt get the answers yet i thiught you had to distribute it then ge tthe answers but now i see that its unnecessary
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
\[\frac4{s^2+4s}=\frac As+\frac B{s+4}\implies A(s+4)+Bs=4\]now plug in\[s=0:A(0+4)+B(0)=4 \implies 4A=4\implies A=1\]
 2 years ago

ranyai12 Group TitleBest ResponseYou've already chosen the best response.0
B=2/3 C=1/6
 2 years ago

ranyai12 Group TitleBest ResponseYou've already chosen the best response.0
thats what I got
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
this is the second term:\[\frac4{s^2+4s}=\frac As+\frac B{s+4}\implies A(s+4)+Bs=4\]now plug in\[s=4:A(4+4)+B(4)=4\implies 4B=4\implies B=1\]
 2 years ago

ranyai12 Group TitleBest ResponseYou've already chosen the best response.0
I didnt get those values though :(
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
do you see how I got mine?
 2 years ago

ranyai12 Group TitleBest ResponseYou've already chosen the best response.0
i mean for the values of the other one
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
that I haven't checked yet, one sec...
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
\[A(s+1)(s+4)+Bs(s+4)+Cs(s+1)=2\]\[s=1:3B=2\implies B=\frac23\]\[s=4:12C=2\implies C=\frac16\]\[s=0:4A=2\implies A=\frac12\]yes I guess you are right :)
 2 years ago

ranyai12 Group TitleBest ResponseYou've already chosen the best response.0
yay!! so would the final answer be (1/2)(2/3)(e^t)+(1/6)e^(4t)e^(4t)
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
looks good to me :)
 2 years ago

ranyai12 Group TitleBest ResponseYou've already chosen the best response.0
it's wrong :(
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
I think you forgot the one from the other term do you have infinite tries?
 2 years ago

ranyai12 Group TitleBest ResponseYou've already chosen the best response.0
no I ownly have 4 more tries
 2 years ago

ranyai12 Group TitleBest ResponseYou've already chosen the best response.0
but what did I forget
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
ok let me try it again from the top; I went of what you had I should doublecheck everything
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
ok I think I found it...
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
\[x''(0)+4x'+8x=2e^{t}\]\[s^2X(s)sx(0)x'(0)+4sX(s)4x(0)+8X(s)=\frac2{s+1}\]\[(s^2+4s+8)X(s)=\frac2{s+1}+4\]
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
you dropped the 8...
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
unfortunately this is going to make partial fractions a real pain...
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
write is as a complete square\[((s+2)^2+4)X(s)=\frac2{s+1}+4\]you should wind up with some hyperbolic I think
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
hyperbolic trig functions*
 2 years ago

ranyai12 Group TitleBest ResponseYou've already chosen the best response.0
can you please show me because I honestly have no clue
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
\[X(s)={2\over{((s+2)^2+4)(s+1)}}+\frac4{((s+2)^2+4)}\]\[={2\over{((s+2)^2+4)(s+1)}}+2\frac2{((s+2)^2+2^2)}\]the second term is form 19 on the chart in your link
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
\[\mathcal L^{1}\{\frac2{((s+2)^2+2^2)}\}=e^{2t}\sin(2t)\]
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
the other part... you're gonna have to use partial fractions fractions and it looks like it's gonna be a pain
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
\[{2\over{((s+2)^2+4)(s+1)}}={As+B\over(s+2)^2+4}+{C\over s+1}\]\[(As+B)(s+1)+C[(s+2)^2+4]=2\]\[s=1:5C=2\implies C=\frac25\]\[s=0:B+\frac{16}5=2\implies B=\frac65\]
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
I think you'll have to get A on your own ;) I'm a bit busy
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
I think\[(A+C)s^2=0\implies A=C=\frac25\]but you shouod doublecheck me
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
I think that is correct
 2 years ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.