 Solution (source code)

by Codex (@codex,  0)

= Solution

Collect the two dependent variables in a column vector. The <vector field> and initial vector are
$$
\boxed{F(x,Z)=\begin{pmatrix}(|z_2|+x^2+1)^{-1}\\(|z_1|+1)^{-1}\end{pmatrix},
\qquad B=\begin{pmatrix}1\\0\end{pmatrix}.}
$$
The given <system of ordinary differential equations> is then $Y'=F(x,Y)$ with $Y(0)=B$. Both components of $F$ are continuous on all of $\mathbb R\times\mathbb R^2$, since their denominators are at least one.

 Back to article page