Internal problem ID [6010]
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: 40.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\relax (t )&=2 x \relax (t )+y \relax (t )+2 z \relax (t )\\ y^{\prime }\relax (t )&=3 x \relax (t )+6 z \relax (t )\\ z^{\prime }\relax (t )&=-4 x \relax (t )-3 z \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.172 (sec). Leaf size: 92
dsolve([diff(x(t),t)=2*x(t)+y(t)+2*z(t),diff(y(t),t)=3*x(t)+6*z(t),diff(z(t),t)=-4*x(t)-3*z(t)],[x(t), y(t), z(t)], singsol=all)
\[ x \relax (t ) = -\frac {{\mathrm e}^{t} \left (\cos \left (2 t \right ) c_{2}+2 \cos \left (2 t \right ) c_{3}+2 \sin \left (2 t \right ) c_{2}-\sin \left (2 t \right ) c_{3}\right )}{2} \] \[ y \relax (t ) = -2 c_{1} {\mathrm e}^{-3 t}-\frac {3 c_{2} {\mathrm e}^{t} \cos \left (2 t \right )}{2}+\frac {3 c_{3} {\mathrm e}^{t} \sin \left (2 t \right )}{2} \] \[ z \relax (t ) = c_{1} {\mathrm e}^{-3 t}+c_{2} {\mathrm e}^{t} \sin \left (2 t \right )+c_{3} {\mathrm e}^{t} \cos \left (2 t \right ) \]
✓ Solution by Mathematica
Time used: 0.026 (sec). Leaf size: 168
DSolve[{x'[t]==2*x[t]+y[t]+2*z[t],y'[t]==3*x[t]+6*z[t],z'[t]==-4*x[t]-3*z[t]},{x[t],y[t],z[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{2} e^t (2 c_1 \cos (2 t)+(c_1+c_2+2 c_3) \sin (2 t)) \\ y(t)\to \frac {1}{5} e^{-3 t} \left (\frac {3}{2} e^{4 t} (2 (2 c_1+c_2+2 c_3) \cos (2 t)+(-3 c_1+c_2+2 c_3) \sin (2 t))-6 c_1+2 c_2-6 c_3\right ) \\ z(t)\to \frac {1}{5} e^{-3 t} \left (e^{4 t} ((-3 c_1+c_2+2 c_3) \cos (2 t)-2 (2 c_1+c_2+2 c_3) \sin (2 t))+3 c_1-c_2+3 c_3\right ) \\ \end{align*}