60.10.24 problem 1937

Internal problem ID [11935]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 9, system of higher order odes
Problem number : 1937
Date solved : Monday, January 27, 2025 at 11:47:26 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*}

✗ Solution by Maple

dsolve([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],singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

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

Not solved