Internal problem ID [6764]
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 }\left (t \right )&=x \left (t \right )-12 y-14 z \left (t \right )\\ y^{\prime }&=x \left (t \right )+2 y-3 z \left (t \right )\\ z^{\prime }\left (t \right )&=x \left (t \right )+y-2 z \left (t \right ) \end {align*}
With initial conditions \[ [x \left (0\right ) = 4, y \left (0\right ) = 6, z \left (0\right ) = -7] \]
✓ Solution by Maple
Time used: 0.031 (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], singsol=all)
\begin{align*} x \left (t \right ) &= -25 \,{\mathrm e}^{t}+11 \sin \left (5 t \right )+29 \cos \left (5 t \right ) \\ y \left (t \right ) &= 7 \,{\mathrm e}^{t}+6 \sin \left (5 t \right )-\cos \left (5 t \right ) \\ z \left (t \right ) &= -6 \,{\mathrm e}^{t}-\cos \left (5 t \right )+6 \sin \left (5 t \right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.016 (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*}