Differential Equations Exam Questions and Answers Graded A+
Differential Equations Exam Questions and Answers Graded A+ Basic steps in creating a model - Answer-1. State assumptions 2. Completely describe the variables and parameters used 3. Use assumptions to derive equations relating quantities 1st Order Equation - Answer-An equation for an unknown function in terms of its derivative: dy/dt=f(t,y) Only contains 1st derivative of dependent variable. Ordinary differential equation - Answer-Does not contain partial derivatives Equilibrium solution - Answer-dP/dt=0 Unlimited population growth model - Answer-dP/dt=kP Limited resources population growth model - Answer-dP/dt=k(1-P/N)P N is the maximum population A solution to a differential equation - Answer-y(t) is a solution if it satisfies dy/dt=y'(t)=f(t,y(t)) An initial value problem - Answer-A differential equation along with an initial condition dy/dt=f(t,y), y(t₀)=y₀ Separable equations - Answer-An equation is separable if the function f(t,y) can be written dy/dt=f(t,y)=g(t)h(y) An autonomous equation (and slope field) - Answer-dy/dt=f(t,y)=h(y) The slope is the same at any t coordinate
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