Question

A system is described by the following differential equation:
$\frac{dy\left(t\right)}{dt}+2y\left(t\right)=\frac{dx\left(t\right)}{dt}+x\left(t\right),$ $x\left(0\right)=y\left(0\right)=0$
where x(t) and y(t) are the input and output variables respectively. The transfer function of the inverse system is

• A. $\frac{s+2}{s+1}$
• B. $\frac{s+1}{s-2}$
• C. $\frac{s-1}{s-2}$
• D. $\frac{s+1}{s+2}$

Answer 1

The correct option is A $\frac{s+2}{s+1}$

$\frac{dy\left(t\right)}{dt}+2y\left(t\right)=\frac{dx\left(t\right)}{dt}+x\left(t\right)$

So, $H\left(s\right)=\frac{Y\left(s\right)}{X\left(s\right)}=\frac{s+1}{s+2}$

So, transfer function of inverse system.

$H^{-1}\left(s\right)=\frac{s+2}{s+1}$