I have a question concerning 1st order ODE's:
Let me assume that we have an ODE $y'(t)=g(y(t))+h(t)$.
And now I am asked to solve it and then determine where the solution is defined. Actually I do not know whether the question "where a solution is defined" is just a property of the parameter or also of the initial condition?- I guess both?
Now I was wondering whether the last thing is just a property of the solution or also of the process of solving this ODE. So what I am actually asking is: How would one do this? My idea was to write down each restriction to the solution that could occur on the way to the solution of the ODE. So if I had to divide by y somewhere but the solution would be totally okay with y=0, I would still have to cross it out.