7.24.8 problem 18

Internal problem ID [608]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 5. Linear systems of differential equations. Section 5.3 (Matrices and linear systems). Problems at page 364
Problem number : 18
Date solved : Monday, January 27, 2025 at 02:56:17 AM
CAS classification : system_of_ODEs

\begin{align*} x^{\prime }&=x t -y \left (t \right )+{\mathrm e}^{t} z \left (t \right )\\ y^{\prime }\left (t \right )&=2 x+t^{2} y \left (t \right )-z \left (t \right )\\ z^{\prime }\left (t \right )&={\mathrm e}^{-t} x+3 y \left (t \right ) t +t^{3} z \left (t \right ) \end{align*}

✗ Solution by Maple

dsolve([diff(x(t),t)=t*x(t)-y(t)+exp(t)*z(t),diff(y(t),t)=2*x(t)+t^2*y(t)-z(t),diff(z(t),t)=exp(-t)*x(t)+3*t*y(t)+t^3*z(t)],singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

DSolve[{D[x[t],t]==t*x[t]-y[t]+Exp[t]*z[t],D[y[t],t]==2*x[t]+t^2y[t]-z[t],D[z[t],t]==Exp[-t]*x[t]+3*t*y[t]+t^3*z[t]},{x[t],y[t],z[t]},t,IncludeSingularSolutions -> True]
 

Not solved