Internal problem ID [10208]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 8, system of first order odes
Problem number: 1885.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} t x^{\prime \prime }\left (t \right )+2 x^{\prime }\left (t \right )+x \left (t \right ) t&=0\\ t x^{\prime }\left (t \right )-y^{\prime }\left (t \right ) t -2 y \left (t \right )&=0 \end {align*}
✓ Solution by Maple
Time used: 0.14 (sec). Leaf size: 50
dsolve([t*diff(x(t),t)-t*diff(y(t),t)-2*y(t)=0,t*diff(x(t),t,t)+2*diff(x(t),t)+t*x(t)=0],singsol=all)
\begin{align*} x \left (t \right ) &= -\frac {c_{3} \cos \left (t \right )-\sin \left (t \right ) c_{2}}{t} \\ y \left (t \right ) &= \frac {-\cos \left (t \right ) c_{3} t +\sin \left (t \right ) c_{2} t +2 c_{2} \cos \left (t \right )+2 \sin \left (t \right ) c_{3} +c_{1}}{t^{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 54
DSolve[{t*x'[t]-t*y'[t]-2*y[t]==0,t*x''[t]+2*x'[t]+t*x[t]==0},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {c_2 \cos (t)+c_3 \sin (t)}{t} \\ y(t)\to \frac {c_2 t \cos (t)+2 c_3 \cos (t)-2 c_2 \sin (t)+c_3 t \sin (t)+c_1}{t^2} \\ \end{align*}