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 : Monday, January 27, 2025 at 06:13:55 AM
CAS classification : system_of_ODEs

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

✗ Solution by Maple

dsolve([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))],singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

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

Not solved