Internal problem ID [15499]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 3 (Systems of differential equations). Section 19. Basic concepts and definitions.
Exercises page 199
Problem number: 767.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\left (t \right )&=-2 t x_{1} \left (t \right )^{2}\\ x_{2}^{\prime }\left (t \right )&=\frac {x_{2} \left (t \right )}{t}+1 \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 23
dsolve([diff(x__1(t),t)=-2*t*x__1(t)^2,diff(x__2(t),t)=(x__2(t)+t)/t],singsol=all)
\begin{align*} \left \{x_{1} \left (t \right ) &= \frac {1}{t^{2}+c_{2}}\right \} \\ \{x_{2} \left (t \right ) &= \left (\ln \left (t \right )+c_{1} \right ) t\} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.143 (sec). Leaf size: 40
DSolve[{x1'[t]==-2*t*x1[t]^2,x2'[t]==(x2[t]+t)/t},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to \frac {1}{t^2-c_1} \\ \text {x2}(t)\to t (\log (t)+c_2) \\ \text {x1}(t)\to 0 \\ \text {x2}(t)\to t (\log (t)+c_2) \\ \end{align*}