# Can anyone help with this, laplace equation -> Y(s) = X(s)(1-s^2)/(1+as+X(s)). I want to get Y(s)/X(s) independent of X(s) on RHS

## 1 Answer

\[Y(s) = \frac{X(s)(1-s^2)}{1+as+X(s)}. (1)\]

Then

\[\frac{Y(s)}{X(s)} = \frac{(1-s^2)}{1+as+X(s)}, (2)\]

and obviously $\frac{Y(s)}{X(s)}$ can not be written solely in terms of $s$. However, you can compute $X(s)$ in terms of $Y(s)$ (using the quadratic formula) and $s$ and substitute $X(s)$ in (2) in terms of $Y(s)$ and $s$. Then you'll have a formula for $\frac{Y(s)}{X(s)}$ independent of $X(s)$, but depending on $Y(s)$, and $s$.

Erdos

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Y/X may depend on Y if you want it to be independent of X. Is that Ok?