60.10.19 problem 1934

Internal problem ID [11854]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 9, system of higher order odes
Problem number : 1934
Date solved : Sunday, March 30, 2025 at 09:18:33 PM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=\frac {x \left (t \right )^{2}}{2}-\frac {y \left (t \right )}{24}\\ \frac {d}{d t}y \left (t \right )&=2 x \left (t \right ) y \left (t \right )-3 z \left (t \right )\\ \frac {d}{d t}z \left (t \right )&=3 x \left (t \right ) z \left (t \right )-\frac {y \left (t \right )^{2}}{6} \end{align*}

✗ Maple

ode:=[diff(x(t),t) = 1/2*x(t)^2-1/24*y(t), diff(y(t),t) = 2*x(t)*y(t)-3*z(t), diff(z(t),t) = 3*x(t)*z(t)-1/6*y(t)^2]; 
dsolve(ode);
 

\[ \text {No solution found} \]

✗ Mathematica

ode={D[x[t],t]==x[t]^2/2-1/24*y[t],D[y[t],t]==2*x[t]*y[t]-3*z[t],D[z[t],t]==3*x[t]*z[t]-1/6*y[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)**2/2 + y(t)/24 + Derivative(x(t), t),0),Eq(-2*x(t)*y(t) + 3*z(t) + Derivative(y(t), t),0),Eq(-3*x(t)*z(t) + y(t)**2/6 + Derivative(z(t), t),0)] 
ics = {} 
dsolve(ode,func=[x(t),y(t),z(t)],ics=ics)
 

NotImplementedError :