I am knew to this site. Hopefully It will end my search.
Let us take a non-linear IVP $dy/dx = (1-2x) y^2$ with $y(0) = y_0$
Now my questions are: (A) Show that this initial value problem has a unique solution for any choice of $y_0$ and (B) How does the interval of definition of the solution depend on $y_0$ ?
Could you explain the procedure to answer those questions? please...