76.10.20 problem 20

Internal problem ID [17542]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 3. Systems of two first order equations. Section 3.6 (A brief introduction to nonlinear systems). Problems at page 195
Problem number : 20
Date solved : Tuesday, January 28, 2025 at 10:40:05 AM
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 )&=x \left (t \right )-\frac {x \left (t \right )^{3}}{5}-\frac {y \left (t \right )}{5} \end{align*}

✗ Solution by Maple

dsolve([diff(x(t),t)=y(t),diff(y(t),t)=x(t)-1/5*x(t)^3-1/5*y(t)],singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[{D[x[t],t]==y[t],D[y[t],t]==x[t]-1/5*x[t]^3-1/5*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

Not solved