EDB — 1QV

Exercises

1. [1QV] Set \(𝛼{\gt}1\) and consider

   \[ \begin{cases} x’ (t) = |x(t)|^𝛼~ ~ , \\ x (t_ 0 ) = x_ 0 ~ ~ \end{cases} \]

   with \(x_ 0,t_ 0∈ℝ\) fixed. Show that there is existence and uniqueness of the solution; calculate the maximal definition interval; Use the variable separation method to explicitly calculate solutions. (Since the equation is autonomous, one could assume that \(t_ 0=0\), but the example is perhaps clearer with a generic \(t_ 0\)).

   Solution 1

   [1QW]↺↻