14.30.5 problem 5

Internal problem ID [2818]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 4. Qualitative theory of differential equations. Section 4.3 (Stability of equilibrium solutions). Page 393
Problem number : 5
Date solved : Monday, January 27, 2025 at 06:14:15 AM
CAS classification : system_of_ODEs

\begin{align*} x^{\prime }&=\tan \left (x+y \left (t \right )\right )\\ y^{\prime }\left (t \right )&=x+x^{3} \end{align*}

✗ Solution by Maple

dsolve([diff(x(t),t)=tan(x(t)+y(t)),diff(y(t),t)=x(t)+x(t)^3],singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

DSolve[{D[x[t],t]==Tan[x[t]+y[t]],D[y[t],t]==x[t]+x[t]^3},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

Not solved