My textbook defines a solution to a differential equation to be a function f(x) such that when substituted into the equation gives a true statement. What I'm confused about are singular solutions. For example the logistic equation: dP/dt = rP(1-P/K) where r and K are constants. My textbook says that P = 0 and P = K are solutions(called equilibrium solutions) since plugging in 0 and K for P give you a true statement, but I thought solutions needed to be functions, not constants. For example why is P = 0 a solution but P = 1 isn't?