Internal problem ID [6011]
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 8.2. Page 346
Problem number: 45.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\relax (t )&=x \relax (t )-12 y \relax (t )-14 z \relax (t )\\ y^{\prime }\relax (t )&=x \relax (t )+2 y \relax (t )-3 z \relax (t )\\ z^{\prime }\relax (t )&=x \relax (t )+y \relax (t )-2 z \relax (t ) \end {align*}
With initial conditions \[ [x \relax (0) = 4, y \relax (0) = 6, z \relax (0) = -7] \]
✓ Solution by Maple
Time used: 0.172 (sec). Leaf size: 62
dsolve([diff(x(t),t) = x(t)-12*y(t)-14*z(t), diff(y(t),t) = x(t)+2*y(t)-3*z(t), diff(z(t),t) = x(t)+y(t)-2*z(t), x(0) = 4, y(0) = 6, z(0) = -7],[x(t), y(t), z(t)], singsol=all)
\[ x \relax (t ) = -25 \,{\mathrm e}^{t}+29 \cos \left (5 t \right )+11 \sin \left (5 t \right ) \] \[ y \relax (t ) = 7 \,{\mathrm e}^{t}+6 \sin \left (5 t \right )-\cos \left (5 t \right ) \] \[ z \relax (t ) = -6 \,{\mathrm e}^{t}+6 \sin \left (5 t \right )-\cos \left (5 t \right ) \]
✓ Solution by Mathematica
Time used: 0.027 (sec). Leaf size: 65
DSolve[{x'[t]==x[t]-12*y[t]-14*z[t],y'[t]==x[t]+2*y[t]-3*z[t],z'[t]==x[t]+y[t]-2*z[t]},{x[0]==4,y[0]==6,z[0]==-7},{x[t],y[t],z[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to -25 e^t+11 \sin (5 t)+29 \cos (5 t) \\ y(t)\to 7 e^t+6 \sin (5 t)-\cos (5 t) \\ z(t)\to -6 e^t+6 \sin (5 t)-\cos (5 t) \\ \end{align*}