52.9.9 problem 9

Internal problem ID [8387]
Book : DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL, WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th edition.
Section : CHAPTER 8 SYSTEMS OF LINEAR FIRST-ORDER DIFFERENTIAL EQUATIONS. EXERCISES 8.1. Page 332
Problem number : 9
Date solved : Monday, January 27, 2025 at 03:53:55 PM
CAS classification : system_of_ODEs

\begin{align*} x^{\prime }\left (t \right )&=x \left (t \right )-y+2 z \left (t \right )+{\mathrm e}^{-t}-3 t\\ y^{\prime }&=3 x \left (t \right )-4 y+z \left (t \right )+2 \,{\mathrm e}^{-t}+t\\ z^{\prime }\left (t \right )&=-2 x \left (t \right )+5 y+6 z \left (t \right )+2 \,{\mathrm e}^{-t}-t \end{align*}

✗ Solution by Maple

dsolve([diff(x(t),t)=x(t)-y(t)+2*z(t)+exp(-t)-3*t,diff(y(t),t)=3*x(t)-4*y(t)+z(t)+2*exp(-t)+t,diff(z(t),t)=-2*x(t)+5*y(t)+6*z(t)+2*exp(-t)-t],singsol=all)
 

\[ \text {No solution found} \]

✓ Solution by Mathematica

Time used: 0.185 (sec). Leaf size: 3251

DSolve[{D[x[t],t]==x[t]-y[t]+2*z[t]+Exp[-t]-3*t,D[y[t],t]==3*x[t]-4*y[t]+z[t]+2*Exp[-t]+t,D[z[t],t]==-2*x[t]+5*y[t]+6*z[t]+2*Exp[-t]-t},{x[t],y[t],z[t]},t,IncludeSingularSolutions -> True]
 

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