EDB — 1RQ

Exercises

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

   $$\{\begin{array}{l}{y}^{\prime }(x)=y(x)(y(x)-x^2)\\ y(2)=1\end{array}$$

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

   $$\underset{x\to -\infty }{lim}y(x)=+\infty ,\underset{x\to \infty }{lim}y(x)=0.$$