82.8.28 problem 36-28 (b)

Internal problem ID [21899]
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 : 36-28 (b)
Date solved : Thursday, October 02, 2025 at 08:05:51 PM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=-x \left (t \right )^{3}-y \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=x \left (t \right ) \end{align*}

✗ Maple

ode:=[diff(x(t),t) = -x(t)^3-y(t), diff(y(t),t) = x(t)]; 
dsolve(ode);
 

\[ \text {No solution found} \]

✗ Mathematica

ode={D[x[t],t]==-x[t]^3-y[t],D[y[t],t]==x[t]}; 
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)**3 + y(t) + Derivative(x(t), t),0),Eq(-x(t) + Derivative(y(t), t),0)] 
ics = {} 
dsolve(ode,func=[x(t),y(t)],ics=ics)
 

NotImplementedError : The given ODE u/(u**3 + v(u)) + Derivative(v(u), u) cannot be solved by the factorable group method