Internal problem ID [10200]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 8, system of first order odes
Problem number: 1877.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-\frac {y \left (t \right )}{t}\\ y^{\prime }\left (t \right )&=-\frac {x \left (t \right )}{t} \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 33
dsolve([t*diff(x(t),t)+y(t)=0,t*diff(y(t),t)+x(t)=0],singsol=all)
\begin{align*} x \left (t \right ) &= \frac {c_{1} t^{2}+c_{2}}{t} \\ y \left (t \right ) &= -\frac {c_{1} t^{2}-c_{2}}{t} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 31
DSolve[{t*x'[t]+y[t]==0,t*y'[t]+x[t]==0},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to c_1 t+\frac {c_2}{t} \\ y(t)\to \frac {c_2}{t}-c_1 t \\ \end{align*}