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Mildred

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About Mildred

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  1. 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
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