Mildred Posted June 19, 2014 Share Posted June 19, 2014 Hi I am not very advanced in calculas. I need to solve for X(t)/Y(t) when t -> infinity. X'(t)+aX(t)+cX(t)-bY(t)=0 ....1 X(0)=0 Y'(t)+bY(t)+cX(t)=0 .....2 Y(0)=0 So I thought of deriving both equations to get: X''(t)+aX'(t)+cX'(t)-bY'(t)=0 ...3 Y''(t)+bY'(t)+cX'(t)=0 ...4 Then substituting 2 into 3 & substituting 1 into 4 X''(t)+aX'(t)+cX'(t)-b*[bY(t)]-bcX(t)=0 ....5 Y''(t)+bY'(t)+cX(t)[a+c]+bY(t)=0 .....6 Then substituting 1 into 5 Then substituting 2 into 6 X''(t)+aX'(t)+cX'(t)+bX'(t)+baX(t)=0 Y''(t)+[a+b+c]Y'(t)+[ab+cb+b]Y(t)=0 Taking the Laplace transform Taking the Laplace transform X(s)[s^2+s+a+c+sa+sc+sb+ba]=0 Y(s)[s^2+sa+2sb+sc+sab+scb-s-b] Then X(s)/Y(s)=[s^2+sa+2sb+sc+sab+scb-s-b]/[s^2+s+a+c+sa+sc+sb+ba] This is where I get stuck as I don't know how to transform it back to get X(t)/Y(t) Any help would be much appreciated. Thank you Link to comment Share on other sites More sharing options...
Bignose Posted June 19, 2014 Share Posted June 19, 2014 You have perform an inverse Laplace transform Link to comment Share on other sites More sharing options...
uncool Posted June 20, 2014 Share Posted June 20, 2014 You can't simply take the inverse transform; the quotient of the transforms isn't the transform of the quotient. However, I'd recommend that you look at the equations just before you take the quotients. You have a full equation for X(s): X(s)[s^2+s+a+c+sa+sc+sb+ba]=0 You should know that X(s) isn't 0 for all s; so that should allow you to "solve" for s. I would note, however, that in this context, the Laplace transform technically shouldn't be applied. Link to comment Share on other sites More sharing options...
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