Internal problem ID [6735]
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: 9.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-x \left (t \right )+y \left (t \right )\\ y^{\prime }\left (t \right )&=x \left (t \right )+2 y \left (t \right )+z \left (t \right )\\ z^{\prime }\left (t \right )&=3 y \left (t \right )-z \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 67
dsolve([diff(x(t),t)=-x(t)+y(t),diff(y(t),t)=x(t)+2*y(t)+z(t),diff(z(t),t)=3*y(t)-z(t)],[x(t), y(t), z(t)], singsol=all)
\[ x \left (t \right ) = -c_{1} {\mathrm e}^{-t}+\frac {{\mathrm e}^{-2 t} c_{2}}{3}+\frac {c_{3} {\mathrm e}^{3 t}}{3} \] \[ y \left (t \right ) = -\frac {{\mathrm e}^{-2 t} c_{2}}{3}+\frac {4 c_{3} {\mathrm e}^{3 t}}{3} \] \[ z \left (t \right ) = c_{1} {\mathrm e}^{-t}+{\mathrm e}^{-2 t} c_{2} +c_{3} {\mathrm e}^{3 t} \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 158
DSolve[{x'[t]==-x[t]+y[t],y'[t]==x[t]+2*y[t]+z[t],z'[t]==3*y[t]-z[t]},{x[t],y[t],z[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{20} e^{-2 t} \left (c_1 \left (15 e^t+e^{5 t}+4\right )+4 c_2 \left (e^{5 t}-1\right )+c_3 \left (-5 e^t+e^{5 t}+4\right )\right ) y(t)\to \frac {1}{5} e^{-2 t} \left (c_1 \left (e^{5 t}-1\right )+c_2 \left (4 e^{5 t}+1\right )+c_3 \left (e^{5 t}-1\right )\right ) z(t)\to \frac {1}{20} e^{-2 t} \left (3 c_1 \left (-5 e^t+e^{5 t}+4\right )+12 c_2 \left (e^{5 t}-1\right )+c_3 \left (5 e^t+3 e^{5 t}+12\right )\right ) \end{align*}