60.10.22 problem 1937

Internal problem ID [11857]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 9, system of higher order odes
Problem number : 1937
Date solved : Sunday, March 30, 2025 at 09:18:35 PM
CAS classification : system_of_ODEs

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

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

NotImplementedError :