A system described by a linear, constant coefficient, ordinary, first order differential equation has an exact solution given by $y(t)$ for $t>0,$ when the forcing function is $x(t)$ and the initial condition is $y(0).$ If one wishes to modify the system so that the solution becomes $-2y(t)$ for $t>0,$ we need to
- change the initial condition to $−y(0)$ and the forcing function to $2x(t)$
- change the initial condition to $2y(0)$ and the forcing function to $−x(t)$
- change the initial condition to $j\sqrt{2}y(0)$ and the forcing function to $j\sqrt{2}x(t)$
- change the initial condition to $−2y(0)$ and the forcing function to $−2x(t)$
