Internal problem ID [9502]
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 }\relax (t )&=-\frac {x \relax (t ) t -y \relax (t )}{t^{2}+1}\\ y^{\prime }\relax (t )&=-\frac {x \relax (t )+y \relax (t ) t}{t^{2}+1} \end {align*}
✓ Solution by Maple
Time used: 0.036 (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)},{x(t), y(t)}, singsol=all)
\[ x \relax (t ) = \frac {c_{1} t +c_{2}}{t^{2}+1} \] \[ y \relax (t ) = \frac {-c_{2} t +c_{1}}{t^{2}+1} \]
✓ Solution by Mathematica
Time used: 0.007 (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*}