Internal problem ID [10246]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 9, system of higher order odes
Problem number: 1923.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-\frac {x \left (t \right ) t}{t^{2}+1}+\frac {y \left (t \right )}{t^{2}+1}\\ y^{\prime }\left (t \right )&=-\frac {t y \left (t \right )}{t^{2}+1}-\frac {x \left (t \right )}{t^{2}+1} \end {align*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 35
dsolve([(t^2+1)*diff(x(t),t)=-t*x(t)+y(t),(t^2+1)*diff(y(t),t)=-x(t)-t*y(t)],singsol=all)
\begin{align*} x \left (t \right ) &= \frac {c_{1} t +c_{2}}{t^{2}+1} \\ y \left (t \right ) &= \frac {-c_{2} t +c_{1}}{t^{2}+1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 39
DSolve[{(t^2+1)*x'[t]==-t*x[t]+y[t],(t^2+1)*y'[t]==-x[t]-t*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {c_2 t+c_1}{t^2+1} \\ y(t)\to \frac {c_2-c_1 t}{t^2+1} \\ \end{align*}