- E15
[1RD] Considering the Cauchy problem
\[ \begin{cases} y’(x) = \frac 1{y(x)^ 2+ x^ 2}\\ y(0)=1 \end{cases} \]show that there is only one global solution \(y:ℝ→ℝ\), that \(y\) is bounded, and the limits \(\lim _{x→∞}y(x)\), \(\lim _{x→-∞}y(x)\) exist and are finite.
![\includegraphics[width=0.9\linewidth ]{UUID/1/R/F/blob_zxx}](/UUID/EDB/1RD/html/images/img-0001.png)
In dashed purple the line of inflections. In yellow the solutions with initial data \(y(0)=1\) and \(y(0)=2\).
Figure 8 Exercise 5. Solution 1
EDB — 1RD
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English
Authors:
"Mennucci , Andrea C. G."
.
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