Internal problem ID [6749]
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: 24.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=3 x \left (t \right )+2 y+4 z \left (t \right )\\ y^{\prime }&=2 x \left (t \right )+2 z \left (t \right )\\ z^{\prime }\left (t \right )&=4 x \left (t \right )+2 y+3 z \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 67
dsolve([diff(x(t),t)=3*x(t)+2*y(t)+4*z(t),diff(y(t),t)=2*x(t)+2*z(t),diff(z(t),t)=4*x(t)+2*y(t)+3*z(t)],singsol=all)
\begin{align*} x \left (t \right ) &= 2 c_{2} {\mathrm e}^{8 t}+2 c_{3} {\mathrm e}^{-t}+{\mathrm e}^{-t} c_{1} \\ y \left (t \right ) &= c_{2} {\mathrm e}^{8 t}+c_{3} {\mathrm e}^{-t} \\ z \left (t \right ) &= 2 c_{2} {\mathrm e}^{8 t}-\frac {5 c_{3} {\mathrm e}^{-t}}{2}-{\mathrm e}^{-t} c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 135
DSolve[{x'[t]==3*x[t]+2*y[t]+4*z[t],y'[t]==2*x[t]+2*z[t],z'[t]==4*x[t]+2*y[t]+3*z[t]},{x[t],y[t],z[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{9} e^{-t} \left (c_1 \left (4 e^{9 t}+5\right )+2 (c_2+2 c_3) \left (e^{9 t}-1\right )\right ) \\ y(t)\to \frac {1}{9} e^{-t} \left (2 c_1 \left (e^{9 t}-1\right )+c_2 \left (e^{9 t}+8\right )+2 c_3 \left (e^{9 t}-1\right )\right ) \\ z(t)\to \frac {1}{9} e^{-t} \left (4 c_1 \left (e^{9 t}-1\right )+2 c_2 \left (e^{9 t}-1\right )+c_3 \left (4 e^{9 t}+5\right )\right ) \\ \end{align*}