EDB — 1RQ

Exercises

1. [1RQ] Note:Exercise 4, written exam 9 July 2011.Show that the Cauchy problem

   \[ \begin{cases} y’(x) = y(x)\big( y(x)-x^ 2\big) \\ y(2)=1 \end{cases} \]

   admits a single solution \(y = y(x)\), defined on all of \(ℝ\) and such that

   \[ \lim _{x→−∞} y(x) = +∞ \quad ,\quad \lim _{x→∞} y(x) = 0 \quad . \]