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Simultaneous Laplace transforms 
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#1
Feb1512, 10:03 PM

P: 20

I have to try and solve the following simultaneous Laplace transform problem and don't really know which path to take can someone give me a nudge in the right direction please.
dx/dt=4x2y & dy/dt=5x+2y given that x(0)=2, y(0)=2 this is what i have so far for dx/dt=4x2y sxx(0)=4x2y sx2=4x2y (s4)x+2y=2 And for dy/dt=5x+2y syy(0)=5x+2y sy+2=5x+2y (s2)y5x=2 Not really sure where to go from here, or even if this is correct. 


#2
Feb1612, 05:42 AM

P: 38

[tex](s4)X+2Y=2,5X(s2)Y=2.[/tex]
[tex]X=\frac{2s}{s^26s+18},Y=\frac{2s18}{s^26s+18}.[/tex] 


#3
Feb1612, 08:56 AM

P: 20

Can you ellaborate a little please.
Where did this all come from? 


#4
Feb1612, 10:10 PM

P: 38

Simultaneous Laplace transforms
##\begin{cases}(s4)X+2Y=2&...(1)\\5X(s2)Y=2&...(2)\end{cases}##
##(s2)\times(1)+2\times(2):((s4)(s2)+10)X=2(s2)+4,##[tex]X=\frac{2s}{s^26s+18}.[/tex] ##5\times(1)(s4)\times(2):(10+(s2)(s4))Y=102(s4),##[tex]Y=\frac{182s}{s^26s+18}.[/tex] 


#5
Feb1612, 11:20 PM

P: 20

Thats great, thanks alot.
Just out of interest where has the 2s in X come from and the 18  2s in Y come from, i can work out the bottom lines. sorry if i appear stupid but it is 5.20am. From there i can use partial fractions to determine the inverse Laplace transform (I think anyway). 


#6
Feb1812, 04:05 PM

P: 20

I get the 2s & the 182s.
Am i correct in thinking these sre complex roots and by definition are quite complex to solve especially the 182s one.? any help is appreciated 


#7
Feb2012, 03:24 PM

P: 20

I need to then try and find the inverse Laplace transform of X & Y can anyone assist me in telling me if i am close with:
X=2e^(3t)*cosh3t Y=e^(18t)2e^(3t)*cosh3t This forum has been more than helpful so far and is highy recommended 


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