Internal problem ID [350]
Book: Differential equations and linear algebra, 4th ed., Edwards and Penney
Section: Section 7.3, The eigenvalue method for linear systems. Page 395
Problem number: problem 47.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\left (t \right )&=23 x_{1} \left (t \right )-18 x_{2} \left (t \right )-16 x_{3} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=-8 x_{1} \left (t \right )+6 x_{2} \left (t \right )+7 x_{3} \left (t \right )+9 x_{4} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=34 x_{1} \left (t \right )-27 x_{2} \left (t \right )-26 x_{3} \left (t \right )-9 x_{4} \left (t \right )\\ x_{4}^{\prime }\left (t \right )&=-26 x_{1} \left (t \right )+21 x_{2} \left (t \right )+25 x_{3} \left (t \right )+12 x_{4} \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 124
dsolve([diff(x__1(t),t)=23*x__1(t)-18*x__2(t)-16*x__3(t)+0*x__4(t),diff(x__2(t),t)=-8*x__1(t)+6*x__2(t)+7*x__3(t)+9*x__4(t),diff(x__3(t),t)=34*x__1(t)-27*x__2(t)-26*x__3(t)-9*x__4(t),diff(x__4(t),t)=-26*x__1(t)+21*x__2(t)+25*x__3(t)+12*x__4(t)],singsol=all)
\begin{align*} x_{1} \left (t \right ) &= c_{1} {\mathrm e}^{3 t}+c_{2} {\mathrm e}^{6 t}+c_{3} {\mathrm e}^{9 t}+c_{4} {\mathrm e}^{-3 t} \\ x_{2} \left (t \right ) &= 2 c_{1} {\mathrm e}^{3 t}+\frac {c_{2} {\mathrm e}^{6 t}}{2}-c_{3} {\mathrm e}^{9 t}+c_{4} {\mathrm e}^{-3 t} \\ x_{3} \left (t \right ) &= -c_{1} {\mathrm e}^{3 t}+\frac {c_{2} {\mathrm e}^{6 t}}{2}+2 c_{3} {\mathrm e}^{9 t}+\frac {c_{4} {\mathrm e}^{-3 t}}{2} \\ x_{4} \left (t \right ) &= c_{1} {\mathrm e}^{3 t}+\frac {c_{2} {\mathrm e}^{6 t}}{2}-c_{3} {\mathrm e}^{9 t}-\frac {c_{4} {\mathrm e}^{-3 t}}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 469
DSolve[{x1'[t]==23*x1[t]-18*x2[t]-16*x3[t]+0*x4[t],x2'[t]==-8*x1[t]+6*x2[t]+7*x3[t]+9*x4[t],x3'[t]==34*x1[t]-27*x2[t]-26*x3[t]-9*x4[t],x4'[t]==-26*x1[t]+21*x2[t]+25*x3[t]+12*x4[t]},{x1[t],x2[t],x3[t],x4[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to \frac {1}{3} e^{-3 t} \left (c_1 \left (9 e^{6 t}-8 e^{9 t}+8 e^{12 t}-6\right )-\left (e^{3 t}-1\right ) \left (6 c_2 \left (e^{3 t}+e^{9 t}+1\right )+c_3 \left (6 e^{3 t}-3 e^{6 t}+7 e^{9 t}+6\right )+3 c_4 e^{6 t} \left (e^{3 t}-1\right )\right )\right ) \\ \text {x2}(t)\to \frac {1}{3} e^{-3 t} \left (-2 c_1 \left (-9 e^{6 t}+2 e^{9 t}+4 e^{12 t}+3\right )+3 c_2 \left (-4 e^{6 t}+e^{9 t}+2 e^{12 t}+2\right )+\left (e^{3 t}-1\right ) \left (c_3 \left (-6 e^{3 t}+12 e^{6 t}+7 e^{9 t}-6\right )+3 c_4 e^{6 t} \left (e^{3 t}+2\right )\right )\right ) \\ \text {x3}(t)\to \frac {1}{3} e^{-3 t} \left (c_1 \left (-9 e^{6 t}-4 e^{9 t}+16 e^{12 t}-3\right )+3 c_2 \left (2 e^{6 t}+e^{9 t}-4 e^{12 t}+1\right )+9 c_3 e^{6 t}+5 c_3 e^{9 t}-14 c_3 e^{12 t}+3 c_4 e^{6 t}+3 c_4 e^{9 t}-6 c_4 e^{12 t}+3 c_3\right ) \\ \text {x4}(t)\to \frac {1}{3} e^{-3 t} \left (c_1 \left (9 e^{6 t}-4 e^{9 t}-8 e^{12 t}+3\right )+3 c_2 \left (-2 e^{6 t}+e^{9 t}+2 e^{12 t}-1\right )-9 c_3 e^{6 t}+5 c_3 e^{9 t}+7 c_3 e^{12 t}-3 c_4 e^{6 t}+3 c_4 e^{9 t}+3 c_4 e^{12 t}-3 c_3\right ) \\ \end{align*}