14.28.4 problem 8

Internal problem ID [2796]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 4. Qualitative theory of differential equations. Section 4.1 (Introduction). Page 377
Problem number : 8
Date solved : Sunday, March 30, 2025 at 12:20:39 AM
CAS classification : system_of_ODEs

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

✓ Maple. Time used: 0.964 (sec). Leaf size: 568

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

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Mathematica. Time used: 23.461 (sec). Leaf size: 20958

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

Too large to display

✗ Sympy

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

NotImplementedError :