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

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

elecengineerBest ResponseYou've already chosen the best response.0
solve the quadratic
 2 years ago

suzi20Best ResponseYou've already chosen the best response.0
yes, im stuck in integral (6+2s) / s(s+2)(s+1)
 2 years ago

math1234Best ResponseYou've already chosen the best response.0
First write everything in terms of the laplace transform. THen solve the equation by converting back.
 2 years ago

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

math1234Best ResponseYou've already chosen the best response.0
Use particla fractions.
 2 years ago

elecengineerBest ResponseYou've already chosen the best response.0
then you must use partial fractions
 2 years ago

suzi20Best ResponseYou've already chosen the best response.0
6+2s = As + B(s+2)+C(s+1) then?
 2 years ago

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

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

elecengineerBest ResponseYou've already chosen the best response.0
partial fractions are very standard
 2 years ago

elecengineerBest ResponseYou've already chosen the best response.0
then you convert them back
 2 years ago

elecengineerBest ResponseYou've already chosen the best response.0
the 3/s goes to 3 from memory
 2 years ago

elecengineerBest ResponseYou've already chosen the best response.0
and the other two are time shifted exponentials
 2 years ago

math1234Best ResponseYou've already chosen the best response.0
Laplace is all about matching and partial fractions, at least in solving simple ODE systems.
 2 years ago

suzi20Best 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?
 2 years ago

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

elecengineerBest 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
 2 years ago

suzi20Best 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?
 2 years ago

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

elecengineerBest ResponseYou've already chosen the best response.0
you make no sense at all lol
 2 years ago

elecengineerBest 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
 2 years ago

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

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

AnwarABest 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 \(y(t)=34e^{t}+e^{2t}\).
 2 years ago

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