Variation-of-constants formula
= Variation-of-constants formula
If $A$ generates $U(t)$, the variation-of-constants formula is
$$
Z(t)=U(t)Z_0+\int_0^tU(t-s)F(s)\,ds.
$$
It is also called Duhamel's formula.
= Variation-of-constants formula
If $A$ generates $U(t)$, the variation-of-constants formula is
$$
Z(t)=U(t)Z_0+\int_0^tU(t-s)F(s)\,ds.
$$
It is also called Duhamel's formula.