I had Dfield8 from MATLAB propose solutions to meeting the following initial conditions:
Now, of course, one of these solutions is non-unique. But, of all of the solutions drawn: do you trust ANY of them? Why or why not?
Note: you really don’t have to do much calculus to see what is wrong with at least one of these. But, if you must know, the general solution is given by (and, of course, the equilibrium solution ). But that really doesn’t provide more information that the differential equation does.
By the way, here are some “correct” plots of the solutions, (up to uniqueness)