- #1
Wiz14
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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?
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?
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