A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 4 years ago
(again)Solve by Laplace transform:
\[\frac{d^2y}{dx^2} + a \frac{dy}{dx}  2a^2y=0\]
y(0)=6, y'(0) = 0
anonymous
 4 years ago
(again)Solve by Laplace transform: \[\frac{d^2y}{dx^2} + a \frac{dy}{dx}  2a^2y=0\] y(0)=6, y'(0) = 0

This Question is Closed

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0\[\frac{d^2y}{dx^2} + a \frac{dy}{dx}  2a^2y=0\]\[sY'0 +a(sY6)2a^2Y=0\]\[s(sY6) +a(sY6)2a^2Y=0\]\[(s^2+as2a^2)Y=6a+6s\]\[Y=\frac{6a+6s}{(s+2a)(sa)}\]So far so good? Or...??

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.1dw:1355844666804:dw

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.1sorry ... i didn't see, looks like the transform of d^2y/dx^2 is incorrect.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0I guess so.. \[L(y'') = s^2Y  s(6) 0=s^2Y6s\]What's wrong?

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.1\[ sY'0 +a(sY6)2a^2Y=0 \] this should be like \[ s^2 Y  6s + a(sY  0) 2a^2 Y = 0 \]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0\[L(\frac{dy}{dx}) = sY  f(0)\]Right?

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.1woops!! sorry I misread ... i put opposite!!

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.1\[ s^2 Y  0  6 + a(sY  6)  2a^2 Y = 0\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0It's okay! But what's wrong with my workings?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0\[L(y'') = s^2Y  s(6) 0=s^2Y6s\]

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.1the second step!! lol ... i again put it wrong!!

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0The second step is right. You just get the third immediately.. \[L(y'') = sL(y')f'(0) = s^2 Ysf(0)  f'(0)\] Anyway.. I still get the third step..?!

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.1Y' ... well i thought you differentiated it.

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.1the answer should be according to mathematica \[ \left\{\left\{y[x]\to 2 e^{2 a x} \left(1+2 e^{3 a x}\right)\right\}\right\} \]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Yes... But I can't get it :(

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.1the final answer is right ... you get \[ F(s) = \frac{6(a+s)}{s^2 + as  2a^2}\] looks lkie you factorized it.

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.1now just take the inverse transform.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Factorize it > partial fraction > inverse Right?

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.1yeah!! that's the way

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0\[F(s) = \frac{6(a+s)}{s^2 + as  2a^2}=\frac{6(a+s)}{(a+2a)(sa)}\]I suppose..

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.1i guess from this point on you get the answer on next step http://www.wolframalpha.com/input/?i=partial+fraction+6%28a%2Bs%29%2F%28s^2+%2B+a+s++2a^2%29 http://www.wolframalpha.com/input/?i=Inverse+Laplace+transform++6%28a%2Bs%29%2F%28s^2+%2B+a+s++2a^2%29

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0\[Y = \frac{6a+6s}{(s+2a)(sa)}=\frac{A}{s+2a}+\frac{B}{sa}\] A(sa) + B(s+2a) =6a+6s A+B = 6 2BA = 6 => B=4 , A=2 \[Y =\frac{2}{s+2a}+\frac{4}{sa}\]\[y=2e^{2at}+4e^{at}\]Why couldn't I get this answer... :\ Thanks!!
Ask your own question
Sign UpFind 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.