Internal problem ID [6716]
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.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-3 x \left (t \right )+4 y+2 \cos \left (t \right ) \sin \left (t \right ) {\mathrm e}^{-t}\\ y^{\prime }&=5 x \left (t \right )+9 z \left (t \right )+8 \cos \left (t \right )^{2} {\mathrm e}^{-t}-4 \,{\mathrm e}^{-t}\\ z^{\prime }\left (t \right )&=y+6 z \left (t \right )-{\mathrm e}^{-t} \end {align*}
✓ Solution by Maple
Time used: 46.781 (sec). Leaf size: 12874
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)],[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: 0.649 (sec). Leaf size: 2949
DSolve[{x'[t]==-3*x[t]+4*y[t]+Exp[-t]*Sin[2*t],y'[t]==5*x[t]+9*z[t]+4*Exp[-t]*Cos[2*t],z'[t]==y[t]+6*z[t]-Exp[-t]},{x[t],y[t],z[t]},t,IncludeSingularSolutions -> True]
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