52.9.8 problem 8

Internal problem ID [8386]
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 : 8
Date solved : Monday, January 27, 2025 at 03:53:17 PM
CAS classification : system_of_ODEs

\begin{align*} x^{\prime }\left (t \right )&=7 x \left (t \right )+5 y-9 z \left (t \right )-8 \,{\mathrm e}^{-2 t}\\ y^{\prime }&=4 x \left (t \right )+y+z \left (t \right )+2 \,{\mathrm e}^{5 t}\\ z^{\prime }\left (t \right )&=-2 y+3 z \left (t \right )+{\mathrm e}^{5 t}-3 \,{\mathrm e}^{-2 t} \end{align*}

✓ Solution by Maple

Time used: 6.787 (sec). Leaf size: 9312

dsolve([diff(x(t),t)=7*x(t)+5*y(t)-9*z(t)-8*exp(-2*t),diff(y(t),t)=4*x(t)+y(t)+z(t)+2*exp(5*t),diff(z(t),t)=-2*y(t)+3*z(t)+exp(5*t)-3*exp(-2*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: 0.202 (sec). Leaf size: 3002

DSolve[{D[x[t],t]==7*x[t]+5*y[t]-9*z[t]-8*Exp[-2*t],D[y[t],t]==4*x[t]+y[t]+z[t]+2*Exp[5*t],D[z[t],t]==-2*y[t]+3*z[t]+Exp[5*t]-3*Exp[-2*t]},{x[t],y[t],z[t]},t,IncludeSingularSolutions -> True]
 

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