14.30.2 problem 2

Internal problem ID [2815]
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 : 2
Date solved : Monday, January 27, 2025 at 06:14:14 AM
CAS classification : system_of_ODEs

\begin{align*} x^{\prime }&=x^{2}+y \left (t \right )^{2}+1\\ y^{\prime }\left (t \right )&=x^{2}-y \left (t \right )^{2} \end{align*}

✗ Solution by Maple

dsolve([diff(x(t),t)=x(t)^2+y(t)^2+1,diff(y(t),t)=x(t)^2-y(t)^2],singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

DSolve[{D[x[t],t]==x[t]^2+y[t]^2+1,D[y[t],t]==x[t]^2-y[t]^2},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

Not solved