Final answer:
The solution to the differential equation dy/dt = -k(y+A) is an exponential decay function, represented as y(t) = Ce^-kt - A, which models processes such as radioactive decay and chemical reaction rates.
Step-by-step explanation:
The student's question relates to finding a solution to the differential equation dy/dt = -k(y+A), where A and k are positive constants. This equation is characteristic of exponential decay processes, which occur in various contexts such as radioactive decay in physics and first-order chemical reactions in chemistry.
The general solution to this differential equation is given by the function y(t) = Ce-kt - A, where C is an integration constant determined by the initial condition. When differentiated with respect to time, this function will yield the original differential equation provided in the question. Also, the integrated rate law represented by [A] = [A]oe-kt aligns with the solution to the differential equation, confirming that as time passes, the concentration of the reactant A follows an exponential decrease.