Internal problem ID [12210]
Internal file name [OUTPUT/10863_Thursday_September_21_2023_05_48_15_AM_75472716/index.tex]
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: 1.
The type(s) of ODE detected by this program : "system of linear ODEs" Unable to solve or complete the solution.
Solve \begin {align*} x^{\prime }\left (t \right )&=y \left (t \right )\\ y^{\prime }\left (t \right )&=\frac {y \left (t \right )^{2}}{x \left (t \right )} \end {align*}
Does not currently support non linear system of equations. This is the phase plot of the system.
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 20
dsolve([diff(x(t),t)=y(t),diff(y(t),t)=y(t)^2/x(t)],singsol=all)
\begin{align*} \{x \left (t \right ) &= {\mathrm e}^{c_{1} t} c_{2}\} \\ \{y \left (t \right ) &= \frac {d}{d t}x \left (t \right )\} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.022 (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*}