Internal problem ID [351]
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 48.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=47 x_{1} \relax (t )-8 x_{2} \relax (t )+5 x_{3} \relax (t )-5 x_{4} \relax (t )\\ x_{2}^{\prime }\relax (t )&=-10 x_{1} \relax (t )+32 x_{2} \relax (t )+18 x_{3} \relax (t )-2 x_{4} \relax (t )\\ x_{3}^{\prime }\relax (t )&=139 x_{1} \relax (t )-40 x_{2} \relax (t )-167 x_{3} \relax (t )-121 x_{4} \relax (t )\\ x_{4}^{\prime }\relax (t )&=-232 x_{1} \relax (t )+64 x_{2} \relax (t )+360 x_{3} \relax (t )+248 x_{4} \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 125
dsolve([diff(x__1(t),t)=47*x__1(t)-8*x__2(t)+5*x__3(t)-5*x__4(t),diff(x__2(t),t)=-10*x__1(t)+32*x__2(t)+18*x__3(t)-2*x__4(t),diff(x__3(t),t)=139*x__1(t)-40*x__2(t)-167*x__3(t)-121*x__4(t),diff(x__4(t),t)=-232*x__1(t)+64*x__2(t)+360*x__3(t)+248*x__4(t)],[x__1(t), x__2(t), x__3(t), x__4(t)], singsol=all)
\[ x_{1} \relax (t ) = -\frac {c_{1} {\mathrm e}^{64 t}}{3}+\frac {c_{2} {\mathrm e}^{16 t}}{2}-2 c_{3} {\mathrm e}^{32 t}+\frac {3 c_{4} {\mathrm e}^{48 t}}{2} \] \[ x_{2} \relax (t ) = -\frac {c_{1} {\mathrm e}^{64 t}}{3}+c_{2} {\mathrm e}^{16 t}-5 c_{3} {\mathrm e}^{32 t}-\frac {c_{4} {\mathrm e}^{48 t}}{2} \] \[ x_{3} \relax (t ) = -\frac {2 c_{1} {\mathrm e}^{64 t}}{3}-\frac {c_{2} {\mathrm e}^{16 t}}{2}-c_{3} {\mathrm e}^{32 t}+\frac {c_{4} {\mathrm e}^{48 t}}{2} \] \[ x_{4} \relax (t ) = c_{1} {\mathrm e}^{64 t}+c_{2} {\mathrm e}^{16 t}+c_{3} {\mathrm e}^{32 t}+c_{4} {\mathrm e}^{48 t} \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 382
DSolve[{x1'[t]==47*x1[t]-8*x2[t]+5*x3[t]-5*x4[t],x2'[t]==-10*x1[t]+32*x2[t]+18*x3[t]-2*x4[t],x3'[t]==139*x1[t]-40*x2[t]-167*x3[t]-121*x4[t],x4'[t]==-232*x1[t]+64*x2[t]+360*x3[t]+248*x4[t]},{x1[t],x2[t],x3[t],x4[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to \frac {1}{16} e^{16 t} \left ((27 c_1-8 c_2-39 c_3-25 c_4) e^{48 t}-2 (19 c_1-8 c_2-31 c_3-17 c_4) e^{16 t}-6 (c_1-5 c_3-3 c_4) e^{32 t}+33 c_1-8 c_2-53 c_3-27 c_4\right ) \\ \text {x2}(t)\to \frac {1}{16} \left (2 (33 c_1-8 c_2-53 c_3-27 c_4) e^{16 t}+(27 c_1-8 c_2-39 c_3-25 c_4) e^{64 t}+2 (c_1-5 c_3-3 c_4) e^{48 t}+(-95 c_1+40 c_2+155 c_3+85 c_4) e^{32 t}\right ) \\ \text {x3}(t)\to \frac {1}{16} e^{16 t} \left (2 (27 c_1-8 c_2-39 c_3-25 c_4) e^{48 t}-2 (c_1-5 c_3-3 c_4) e^{32 t}+(-19 c_1+8 c_2+31 c_3+17 c_4) e^{16 t}-33 c_1+8 c_2+53 c_3+27 c_4\right ) \\ \text {x4}(t)\to \frac {1}{16} \left (2 (33 c_1-8 c_2-53 c_3-27 c_4) e^{16 t}+(19 c_1-8 c_2-31 c_3-17 c_4) e^{32 t}-4 (c_1-5 c_3-3 c_4) e^{48 t}+(-81 c_1+24 c_2+117 c_3+75 c_4) e^{64 t}\right ) \\ \end{align*}