I have integral and differential inequality
$y'(t)<Ch^{k+1}+\int_0^ty(s)ds+y(t)$
where $C,h$ are constants and $y$ is positive function with y(0)=0
My goal is to prove
$y(t_F)<Ch^{k+1}$ where $t_F$ is final time
Is it possible? At first, I misread the equation as without integration. At that time, Gronwall's inequality was enough. However, becaus of that integration on the right hand side, I don't know how to prove this anymore.
Is there any theorem for such integral differential inequality?