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suzi20
 3 years ago
y" + 3y' + 2y = 6 y(0)=0 y'(0) = 2
with laplace
suzi20
 3 years ago
y" + 3y' + 2y = 6 y(0)=0 y'(0) = 2 with laplace

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

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

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

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

math1234
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.0no, so you got y to be that

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

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

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

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

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

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

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

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

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

math1234
 3 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
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.01/(sa) = e^(at) ( I googled this lol )

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

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

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