A community for students.
Here's the question you clicked on:
 0 viewing
suzi20
 4 years ago
y" + 3y' + 2y = 6 y(0)=0 y'(0) = 2
with laplace
suzi20
 4 years ago
y" + 3y' + 2y = 6 y(0)=0 y'(0) = 2 with laplace

This Question is Closed

elecengineer
 4 years ago
Best ResponseYou've already chosen the best response.0y'' = sy^2  sy(0) y'(0)

elecengineer
 4 years ago
Best ResponseYou've already chosen the best response.0(sy^2 2) +3(sy) +2y = 6

elecengineer
 4 years ago
Best ResponseYou've already chosen the best response.0solve the quadratic

suzi20
 4 years ago
Best ResponseYou've already chosen the best response.0yes, im stuck in integral (6+2s) / s(s+2)(s+1)

math1234
 4 years ago
Best ResponseYou've already chosen the best response.0First write everything in terms of the laplace transform. THen solve the equation by converting back.

elecengineer
 4 years ago
Best ResponseYou've already chosen the best response.0no, so you got y to be that

math1234
 4 years ago
Best ResponseYou've already chosen the best response.0Use particla fractions.

elecengineer
 4 years ago
Best ResponseYou've already chosen the best response.0then you must use partial fractions

suzi20
 4 years ago
Best ResponseYou've already chosen the best response.06+2s = As + B(s+2)+C(s+1) then?

elecengineer
 4 years ago
Best ResponseYou've already chosen the best response.0= 3/s 4/(s+1) +1/(s+2)

elecengineer
 4 years ago
Best ResponseYou've already chosen the best response.0I created and went straight to wolframa for the partial fractions

elecengineer
 4 years ago
Best ResponseYou've already chosen the best response.0partial fractions are very standard

elecengineer
 4 years ago
Best ResponseYou've already chosen the best response.0then you convert them back

elecengineer
 4 years ago
Best ResponseYou've already chosen the best response.0the 3/s goes to 3 from memory

elecengineer
 4 years ago
Best ResponseYou've already chosen the best response.0and the other two are time shifted exponentials

math1234
 4 years ago
Best ResponseYou've already chosen the best response.0Laplace is all about matching and partial fractions, at least in solving simple ODE systems.

suzi20
 4 years ago
Best ResponseYou've already chosen the best response.06+2s = As + B(s+2)+C(s+1) s=1 > 4 = A+B s=2 > 2 = 2AC for the last s what number should i choose?

elecengineer
 4 years ago
Best ResponseYou've already chosen the best response.01/(sa) = e^(at) ( I googled this lol )

elecengineer
 4 years ago
Best ResponseYou've already chosen the best response.0remember you can pick any value for s, just that some values will make the simultaneous eqns alot easierto solve

suzi20
 4 years ago
Best ResponseYou've already chosen the best response.06+2s = As + B(s+2)+C(s+1) s=1 > 4 = A+B s=2 > 2 = 2AC s=0 > 6 = 2B+C  4+A = B 6 = 2(4+A)+C 6 = 8 +2A+C elimination 2 = 2A+C 2 = 2A C infinity?

elecengineer
 4 years ago
Best ResponseYou've already chosen the best response.0y= 34e^(t) + e^(2t)

elecengineer
 4 years ago
Best ResponseYou've already chosen the best response.0you make no sense at all lol

elecengineer
 4 years ago
Best ResponseYou've already chosen the best response.0this is why people need to pay attention in high school and first year uni maths course , so they absolutely hammer in the basics

elecengineer
 4 years ago
Best ResponseYou've already chosen the best response.0its just simultaneous eqns , takes for ever, you need to set up a matrix etc.

elecengineer
 4 years ago
Best ResponseYou've already chosen the best response.0it will take me like 10mins to type it up , I aint doing it lol

AnwarA
 4 years ago
Best ResponseYou've already chosen the best response.1I can see that you reach the point \(Y(s)=\frac{2s+6}{s(s+1)(s+2)}\). Now we should use partial fractions to write the expression in a form that can be easily to find its inverse laplace transform. That's \[{2s+6 \over s(s+1)(s+2)}={a \over s}+{b \over s+1}+{c \over s+2}\]. Multiplying both sides by \(s(s+1)(s+2)\) gives: \[2s+6=a(s+1)(s+2)+bs(s+2)+cs(s+1)\] Plugging \(s=0\) gives \(2a=6 \implies a=3\); \(s=1\) gives \(b=4 \implies b=4\), and \(s=2\) gives \(2c=2 \implies c=1\). So, \(Y(s)=3\frac{1}{s}\frac{4}{s+1}+\frac{1}{s+2}\). Hence \(y(t)=34e^{t}+e^{2t}\).

AnwarA
 4 years ago
Best ResponseYou've already chosen the best response.1Hello suzi!! Does the answer make sense to you?
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.