I have ODE course in my university this year. Our teacher gave us a problem in the first lesson and said that if we solve it, we'll have an advantage in the exam. Probably the task is too difficult and he is joking. So here it is:
We have an ODE: $$y^\prime = y^2+x$$ I need to prove:
- Phase lines have a vertical asymptotes in the left and on the right.
- Upper part of x=-y^2 is asymptote. (I add a pic of it)
- Prove that there is only one phase curve without vertical asymptote(Toughest question).
Any ideas, links and explanations are welcome. Thank you.
