A B C D E

Exercises relating to fundamental properties of ODEs.

Trace the solution of the given ODE which begins at the point A. Which of the other
labelled points will the solution pass through?

B C D E

The ODE has one asymptotically stable constant solution. It is
Trace the solution of the given ODE which begins at the point A. Which of the other
labelled points will the solution pass through?

B C D E

The ODE has noonetwothree
constant solutions.
Let be the solution to the initial value problem with . Use Euler’s Method
with step size to approximate the value of . Fill in your work in the table
below.

Let be the solution to the initial value problem with . Use Euler’s Method
with step size to approximate the value of . Fill in your work in the table
below.

Is the function a solution of the ODE ?

Yes No

If yes, is it a solution of the IVP and ? Yes No Not applicable

Is the function a solution of the IVP and ? Yes No

Given this, what is the difference between the approximated value of that you
calculated and the exact value. If you get a negative answer, take its absolute value: