76.10.18 problem 18

Internal problem ID [17540]
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 : 18
Date solved : Tuesday, January 28, 2025 at 10:40:04 AM
CAS classification : system_of_ODEs

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

✗ Solution by Maple

dsolve([diff(x(t),t)=(2+x(t))*(y(t)-x(t)),diff(y(t),t)=y(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]==(2+x[t])*(y[t]-x[t]),D[y[t],t]==y[t]-x[t]^2-y[t]^2},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

Not solved