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

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.

## Comments

^{-πs/s }+ s, or (b) 1/s - e^{-πs/(s + s)}, or (c) 1/s - e^{-πs}/s + s.