怎么证明这个系统是线性的？

sunyuanxin

The initial reset assumption corresponds toa zero-valued auxiliary condition/being imposed at a time determined inaccordance with the input signal. In the problem we show that if the auxiliarycondition used is nonzero, or if it is always applied at a fixed-time(regardlessof the input signal)the corresponding system can not be LTI. Consider a systemwhose input x(t)and output y(t)satisfy the first-order differential equation dy(t)/dt+2y(t)=x(t).

Given the auxiliary condition y(0)+y(4)=0,showthat the system is linear but not time invariant.