82.8.31 problem 36-31

Internal problem ID [21902]
Book : The Differential Equations Problem Solver. VOL. II. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 36. Nonlinear differential equations. Page 1203
Problem number : 36-31
Date solved : Sunday, October 12, 2025 at 05:51:37 AM
CAS classification : system_of_ODEs

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

✓ Maple. Time used: 1.141 (sec). Leaf size: 439

ode:=[diff(x(t),t) = -x(t)+y(t)^2, diff(y(t),t) = -y(t)+x(t)^2]; 
dsolve(ode);
 

\begin{align*} \text {Solution too large to show}\end{align*}

✗ Mathematica

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

Not solved

✗ Sympy

from sympy import * 
t = symbols("t") 
x = Function("x") 
y = Function("y") 
ode=[Eq(x(t) - y(t)**2 + Derivative(x(t), t),0),Eq(-x(t)**2 + y(t) + Derivative(y(t), t),0)] 
ics = {} 
dsolve(ode,func=[x(t),y(t)],ics=ics)
 

Timed Out