Internal problem ID [10242]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 8, system of first order odes
Problem number: 1910.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=\frac {2 x \left (t \right )}{t}-1\\ y^{\prime }\left (t \right )&=\frac {y \left (t \right )}{t}-\frac {x \left (t \right )}{t^{3}}+\frac {1}{t^{2}}\\ z^{\prime }\left (t \right )&=\frac {z \left (t \right )}{t}-\frac {y \left (t \right )}{t^{2}}-\frac {x \left (t \right )}{t^{4}}+\frac {1}{t^{3}} \end {align*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 37
dsolve([t*diff(x(t),t)=2*x(t)-t,t^3*diff(y(t),t)=-x(t)+t^2*y(t)+t,t^4*diff(z(t),t)=-x(t)-t^2*y(t)+t^3*z(t)+t],[x(t), y(t), z(t)], singsol=all)
\[ x \left (t \right ) = c_{2} t^{2}+t \] \[ y \left (t \right ) = c_{1} t +c_{2} \] \[ z \left (t \right ) = \frac {c_{3} t^{2}+c_{1} t +c_{2}}{t} \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 39
DSolve[{t*x'[t]==2*x[t]-t,t^3*y'[t]==-x[t]+t^2*y[t]+t,t^4*z'[t]==-x[t]-t^2*y[t]+t^3*z[t]+t},{x[t],y[t],z[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to t (1+c_3 t) y(t)\to c_2 t+c_3 z(t)\to c_1 t+\frac {c_3}{t}+c_2 \end{align*}