66.3.4 problem Problem 5

Internal problem ID [13947]
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
Date solved : Tuesday, January 28, 2025 at 08:24:56 PM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=y \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=\frac {y \left (t \right )^{2}}{x \left (t \right )} \end{align*}

✓ Solution by Maple

Time used: 0.528 (sec). Leaf size: 19

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: 0.018 (sec). Leaf size: 28

DSolve[{D[x[t],t]==y[t],D[y[t],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*}