Past exam of the algebra, analysis and differential equations 1 course of the University of Oxford / 2013 / Differential Equations / 7 / a

Collect the two dependent variables in a column vector. The vector field and initial vector areThe given system of ordinary differential equations is then $Y^{\prime }=F(x,Y)$ 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.