A community for students. Sign up today!
Here's the question you clicked on:
 0 viewing
 2 years ago
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
Help Please!! Use Laplace transforms to solve the initial value problem x''+4x'+8x=2e^(t) ; x(0)=0 and x'(0)=4

This Question is Closed

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

TuringTest
 2 years ago
Best 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\[s=0:A(0+4)+B(0)=4 \implies 4A=4\implies A=1\]

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

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

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

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

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

TuringTest
 2 years ago
Best 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 :)

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

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

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

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

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

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

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

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

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

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

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

TuringTest
 2 years ago
Best 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

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

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

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

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

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

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.0I think that is correct
Ask your own question
Ask a QuestionFind more explanations on OpenStudy
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.