The domain of a solution and stability of solutions of a differential equation.

A. Find all the solutions.
B. For which values of y0 does the solution defined on the entire real line not exist? What is the maximum domain in which a solution exists in this case?
C. For what values of y0 does more than one solution pass through the point (0,y0)? Write down all the solutions that go through it in this case.
D. Each point y0 through which a fixed solution passes is called a "setpoint". Find the setpoints and determine whether they are stable/asymptotically stable solutions.
  • Erdos Erdos

    This is a a multi-part high level question that can easily take about an hour to answer. The offered bounty is too low!

    • Erdos Erdos

      Offer is still low! Your offer should be high enough to provide enough incentive for someone to spend their time to write a good solution.

  • 20$ is all I got. If someone were kind enough to accept this offer it would be nice, but unfortunately, I don't have any more


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Erdos Erdos
  • Can you prove that the solutions are unstable by definition of stability?

    • Erdos Erdos

      This is how the stability is done for solutions of ODEs. It's rare to use the definition to prove it.

  • What about y=-1? Is it also a solution or I'm mistaken?

    • Erdos Erdos

      You are right. $y=-1$ is also an unstable solution. I revised the solution.

The answer is accepted.
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