Problem 3
Explain how the growth rate function can be decreasing while the population function is increasing.
Problem 3
Does the function \(y(t)=2 t\) satisfy the differential equation \(y^{\prime \prime \prime}(t)+y^{\prime}(t)=2 ?\)
Problem 3
Consider the initial value problem \(y^{\prime}(t)=t^{2}-3 y^{2}, y(3)=1\) What is the approximation to \(y(3.1)\) given by Euler's method with a time step of \(\Delta t=0.1 ?\)
Problem 4
Explain how a stirred tank reaction works.
Problem 4
Give a geometrical explanation of how Euler's method works.
Problem 4
Does the function \(y(t)=6 e^{-3 t}\) satisfy the initial value problem \(y^{\prime}(t)-3 y(t)=0, y(0)=6 ?\)
Problem 4
Explain how to solve a separable differential equation of the form \(g(t) y^{\prime}(t)=h(t)\).
Problem 4
What is the equilibrium solution of the equation \(y^{\prime}(t)=3 y-9 ?\) Is it stable or unstable?
Problem 5
Find the general solution of the following equations. $$y^{\prime}(t)=3 y-4$$
Problem 5
Is the differential equation that describes a stirred tank reaction (as developed in this section) linear or nonlinear? What is its order?
