60.10.21 problem 1934

Internal problem ID [11932]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 9, system of higher order odes
Problem number : 1934
Date solved : Monday, January 27, 2025 at 11:47:25 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*}

✗ Solution by Maple

dsolve([diff(x(t),t)=x(t)^2/2-1/24*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],singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[{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},{x[t],y[t],z[t]},t,IncludeSingularSolutions -> True]
 

Not solved