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

elecengineer Group TitleBest ResponseYou've already chosen the best response.0
y' = sy  y(0)
 3 years ago

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

elecengineer Group TitleBest ResponseYou've already chosen the best response.0
solve the quadratic
 3 years ago

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

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

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

math1234 Group TitleBest ResponseYou've already chosen the best response.0
Use particla fractions.
 3 years ago

elecengineer Group TitleBest ResponseYou've already chosen the best response.0
then you must use partial fractions
 3 years ago

suzi20 Group TitleBest ResponseYou've already chosen the best response.0
6+2s = As + B(s+2)+C(s+1) then?
 3 years ago

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

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

elecengineer Group TitleBest ResponseYou've already chosen the best response.0
cheated
 3 years ago

elecengineer Group TitleBest ResponseYou've already chosen the best response.0
partial fractions are very standard
 3 years ago

elecengineer Group TitleBest ResponseYou've already chosen the best response.0
then you convert them back
 3 years ago

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

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

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

suzi20 Group TitleBest ResponseYou've already chosen the best response.0
6+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?
 3 years ago

elecengineer Group TitleBest ResponseYou've already chosen the best response.0
1/(sa) = e^(at) ( I googled this lol )
 3 years ago

elecengineer Group TitleBest ResponseYou've already chosen the best response.0
s=0 lol
 3 years ago

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

suzi20 Group TitleBest ResponseYou've already chosen the best response.0
6+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?
 3 years ago

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

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

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

suzi20 Group TitleBest ResponseYou've already chosen the best response.0
could u help me?
 3 years ago

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

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

suzi20 Group TitleBest ResponseYou've already chosen the best response.0
matrix? really?
 3 years ago

AnwarA Group TitleBest ResponseYou've already chosen the best response.1
I 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 \(y(t)=34e^{t}+e^{2t}\).
 3 years ago

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

suzi20 Group TitleBest ResponseYou've already chosen the best response.0
thank you anwara
 3 years ago

AnwarA Group TitleBest ResponseYou've already chosen the best response.1
You're welcome!
 3 years ago
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