This is a very basic problem. Or, when we accept that the brain solves differential equations, we must say how the brain solves integration, as integration is basic operation necessary for solution to differential equations. Brain tissue consists of neurons, their connections and the insulating material we know as glia. Some scientists were thinking about data processing inside of neurons. They thought that neurons are processors having some internal data processing.
Neurons are only cells having different characteristics than other cells.
These differences are not so dramatic that we should suppose that neurons work like integrators. In spite of that, it seems to be very clear that most deductions can be correct. Differential equations describe movement. Integration is the basic operation that is used to solve differential equations. The human brain must be able to solve integration using neural structures.