Motivated by important applications in materials science and biology, we consider a non-stationary coagulation equation with in-flux and out-flux of particles (cargo). An exact analytical solution to this integrodifferential equation is found in a parametric form. This solution behaves as a decaying exponent with respect to the particle volume (fluorescence intensity in the case of coagulation of endosomes). We demonstrate that our exact solution substantially depends on coagulation kernels (fusion and fission rates) as well as the in-flux and out-flux processes of cargo.