Internal problem ID [5965]
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.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\relax (t )&=7 x \relax (t )+5 y \relax (t )-9 z \relax (t )-8 \,{\mathrm e}^{-2 t}\\ y^{\prime }\relax (t )&=4 x \relax (t )+y \relax (t )+z \relax (t )+2 \,{\mathrm e}^{5 t}\\ z^{\prime }\relax (t )&=-\left (-{\mathrm e}^{7 t}-3 z \relax (t ) {\mathrm e}^{2 t}+2 y \relax (t ) {\mathrm e}^{2 t}+3\right ) {\mathrm e}^{-2 t} \end {align*}
✓ Solution by Maple
Time used: 22.641 (sec). Leaf size: 11902
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)],[x(t), y(t), z(t)], singsol=all)
\[ \text {Expression too large to display} \] \[ \text {Expression too large to display} \] \[ \text {Expression too large to display} \]
✓ Solution by Mathematica
Time used: 0.246 (sec). Leaf size: 3002
DSolve[{x'[t]==7*x[t]+5*y[t]-9*z[t]-8*Exp[-2*t],y'[t]==4*x[t]+y[t]+z[t]+2*Exp[5*t],z'[t]==-2*y[t]+3*z[t]+Exp[5*t]-3*Exp[-2*t]},{x[t],y[t],z[t]},t,IncludeSingularSolutions -> True]
Too large to display