Internal problem ID [10863]
Book: Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS,
MOSCOW, Third printing 1977.
Section: Chapter 3, SYSTEMS OF DIFFERENTIAL EQUATIONS. Problems page 209
Problem number: Problem 5.
ODE order: 1.
ODE degree: 2.
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 38
dsolve([diff(x(t),t)=y(t),diff(y(t),t)=y(t)^2/x(t)],[x(t), y(t)], singsol=all)
\begin{align*} \{y \left (t \right ) = 0\} \\ \{x \left (t \right ) = c_{1}\} \\ \end{align*} \begin{align*} \{y \left (t \right ) = {\mathrm e}^{c_{1} t} c_{2}\} \\ \left \{x \left (t \right ) = \frac {y \left (t \right )^{2}}{\frac {d}{d t}y \left (t \right )}\right \} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 28
DSolve[{x'[t]==y[t],y'[t]==y[t]^2/x[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to c_1 c_2 e^{c_1 t} \\ x(t)\to c_2 e^{c_1 t} \\ \end{align*}