MATH 1132Q Lecture Notes - Lecture 21: Constant Function
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Math 1132q , lecture 21 , section 9. 1 -- modeling with differential equations. Let y = f(x) be a function that models the population of egrets on an island. This is an example of a differential equation: an equation that involves a function y and its derivatives y", y"". Solving a differential equation means finding functions y that satisfy the given equation. Suppose we know that y" = y (a) what"s a function that satisfies the differential equation above? y = e^ x y" = e^ x = y. [ equilibrium solution: a solution that"s a constant function ] (c) suppose we also know that y(0) = 70 , the initial population is 70 (this is an initial condition ). What solution to our equation satisfies this condition? x = 0 , y = 70 y = 0 y = ce^ x. 70 = c e^0 = 1 y = 70 e^ x and.
