Solving integral time dependant equation

Question

I am stuck with this problem and I am not sure whether it is possible to solve it.

$$c(t)-\frac{\int c(t) \dot{O}(t) dt}{V_G} = \frac{V}{V_G}$$ The variable of interest is $c(t)$.

I would appreciate it if someone could give me a clue.

Answer 1

Derivate the equation to get $$ \frac{dc}{dt}-\frac{1}{V_G}\,c\,\dot O=0. $$ This is a first order linear differential equation.