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How to solve for Y(s)?

Y(s)(s^2+s+5/4)=1/s-e^(-pi*s)/s+s

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Please make sure all parentheses are correct. For example, the right hand side of the equation could be:
 
(a) 1/s - e-πs/s + s, or (b)  1/s - e-πs/(s + s), or (c) 1/s - e-πs/s + s. 
 
Because (a) and (b) can be simplified, I'm going to guess it's (c). However, there could be other options.
Well, (c) can be simplified, too, but it's not as apparent.

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1 Answer

To solve for Y(s), you would divide by the factor (s²+s+5/4):
 
Y(s) = ( 1/s-e^(-pi*s)/s+s )/(s²+s+5/4).
 
I'm assuming there is more to this problem. Your equation looks like the Laplace transform of a differential equation. Are you supposed to find the inverse transform, f(t) ? If so, you would complete the square in the denominator,
s²+s+5/4 = (s+1/2)² + 1,
then split the fraction into three terms, then use standard tables to find the inverse transform.

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Y(s) = ( 1/s-e^(-pi*s)/s+s )/(s²+s+5/4)

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