87.30.15 problem 15

Internal problem ID [23914]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 8. Nonlinear differential equations and systems. Exercise at page 310
Problem number : 15
Date solved : Thursday, October 02, 2025 at 09:46:30 PM
CAS classification : system_of_ODEs

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

✗ Maple

ode:=[diff(x(t),t) = y(t)+x(t)^2-x(t)*y(t), diff(y(t),t) = -2*x(t)+3*y(t)+y(t)^2]; 
dsolve(ode);
 

\[ \text {No solution found} \]

✗ Mathematica

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

Timed Out