Internal problem ID [9457]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 8, system of first order odes
Problem number: 1878.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\relax (t )&=-\frac {2 x \relax (t )-t}{t}\\ y^{\prime }\relax (t )&=\frac {x \relax (t ) t +y \relax (t ) t +2 x \relax (t )-t}{t} \end {align*}
✓ Solution by Maple
Time used: 0.081 (sec). Leaf size: 39
dsolve({t*diff(x(t),t)+2*x(t)=t,t*diff(y(t),t)-(t+2)*x(t)-t*y(t)=-t},{x(t), y(t)}, singsol=all)
\[ x \relax (t ) = \frac {t}{3}+\frac {c_{2}}{t^{2}} \] \[ y \relax (t ) = \frac {3 c_{1} {\mathrm e}^{t} t^{2}-t^{3}-3 c_{2}}{3 t^{2}} \]
✓ Solution by Mathematica
Time used: 0.03 (sec). Leaf size: 39
DSolve[{t*x'[t]+2*x[t]==t,t*y'[t]-(t+2)*x[t]-t*y[t]==-t},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {t}{3}+\frac {c_1}{t^2} \\ y(t)\to -\frac {c_1}{t^2}-\frac {t}{3}+c_2 e^t \\ \end{align*}