Internal problem ID [10202]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 8, system of first order odes
Problem number: 1879.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-\frac {2 x \left (t \right )}{t}+\frac {2 y \left (t \right )}{t}+1\\ y^{\prime }\left (t \right )&=t -\frac {x \left (t \right )}{t}-\frac {5 y \left (t \right )}{t} \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 54
dsolve([t*diff(x(t),t)+2*(x(t)-y(t))=t,t*diff(y(t),t)+x(t)+5*y(t)=t^2],singsol=all)
\begin{align*} x \left (t \right ) &= \frac {2 t^{6}+9 t^{5}+30 c_{1} t +30 c_{2}}{30 t^{4}} \\ y \left (t \right ) &= -\frac {-8 t^{6}+3 t^{5}+30 c_{1} t +60 c_{2}}{60 t^{4}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.032 (sec). Leaf size: 58
DSolve[{t*x'[t]+2*(x[t]-y[t])==t,t*y'[t]+x[t]+5*y[t]==t^2},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {c_1}{t^4}+\frac {c_2}{t^3}+\frac {1}{30} t (2 t+9) \\ y(t)\to -\frac {-8 t^6+3 t^5+30 c_2 t+60 c_1}{60 t^4} \\ \end{align*}