14.28.3 problem 7

Internal problem ID [2795]
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 : 7
Date solved : Sunday, March 30, 2025 at 12:20:38 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=-1-y \left (t \right )-{\mathrm e}^{x \left (t \right )}\\ \frac {d}{d t}y \left (t \right )&=x \left (t \right )^{2}+y \left (t \right ) \left ({\mathrm e}^{x \left (t \right )}-1\right )\\ \frac {d}{d t}z \left (t \right )&=x \left (t \right )+\sin \left (z \left (t \right )\right ) \end{align*}

✗ Maple

ode:=[diff(x(t),t) = -1-y(t)-exp(x(t)), diff(y(t),t) = x(t)^2+y(t)*(exp(x(t))-1), diff(z(t),t) = x(t)+sin(z(t))]; 
dsolve(ode);
 

\[ \text {No solution found} \]

✗ Mathematica

ode={D[x[t],t]==-1-y[t]-Exp[x[t]],D[y[t],t]==x[t]^2+y[t]*(Exp[x[t]]-1),D[z[t],t]==x[t]+Sin[z[t]]}; 
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(y(t) + exp(x(t)) + Derivative(x(t), t) + 1,0),Eq((1 - exp(x(t)))*y(t) - x(t)**2 + Derivative(y(t), t),0),Eq(-x(t) - sin(z(t)) + Derivative(z(t), t),0)] 
ics = {} 
dsolve(ode,func=[x(t),y(t),z(t)],ics=ics)
 

NotImplementedError :