Initial-Value Problem for System of Differential Equations : Fundamental Theorem of Calculus
Let Q(t) =< (less than or equal) C + integral from t_0 to t ( K(s) Q(s) ) ds,
Where Q(t) is a nonegative function , C > 0 and K(s) >= 0.
Q(t) =< Ce^( integral from t_0 to t ( K(s)ds) ), t >= t_0
b). What conclusion can be made if C = 0? ( Note that proof in a may fail is C = 0 ).
I want a detailed proof, please justify every claim you make. Thanks.