- Now we will obtain the solution
to the initial value problem
dy/dt = sin(y), with
y(0) = 0.1.
Plot the direction field, and
then use your helper application's built-in differential equation solver to
plot the solution to the initial value problem. (Be careful with the dimensions
of the plot window.)
- Rather than attempting to solve
the equation symbolically, discuss why the graph of the solution has the form
you see. In particular, why does it look so similar to the solution of the
corresponding initial value problem for the Logistic Equation?
- Describe all equilibrium
solutions (i.e., constant solutions) of
dy/dt = sin(y).
- Find an initial value b
for y(0) so that the solution of the initial value problem
dy/dt = sin(y), with
y(0) = b
does not resemble a solution
of the Logistic Equation.
