52.9.6 problem 6

Internal problem ID [8384]
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 : 6
Date solved : Monday, January 27, 2025 at 03:50:16 PM
CAS classification : system_of_ODEs

\begin{align*} x^{\prime }\left (t \right )&=-3 x \left (t \right )+4 y+{\mathrm e}^{-t} \sin \left (2 t \right )\\ y^{\prime }&=5 x \left (t \right )+9 z \left (t \right )+4 \,{\mathrm e}^{-t} \cos \left (2 t \right )\\ z^{\prime }\left (t \right )&=y+6 z \left (t \right )-{\mathrm e}^{-t} \end{align*}

✓ Solution by Maple

Time used: 9.200 (sec). Leaf size: 6445

dsolve([diff(x(t),t)=-3*x(t)+4*y(t)+exp(-t)*sin(2*t),diff(y(t),t)=5*x(t)+9*z(t)+4*exp(-t)*cos(2*t),diff(z(t),t)=y(t)+6*z(t)-exp(-t)],singsol=all)
 

\begin{align*} \text {Expression too large to display} \\ \text {Expression too large to display} \\ \text {Expression too large to display} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.534 (sec). Leaf size: 2949

DSolve[{D[x[t],t]==-3*x[t]+4*y[t]+Exp[-t]*Sin[2*t],D[y[t],t]==5*x[t]+9*z[t]+4*Exp[-t]*Cos[2*t],D[z[t],t]==y[t]+6*z[t]-Exp[-t]},{x[t],y[t],z[t]},t,IncludeSingularSolutions -> True]
 

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