Internal problem ID [346]
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 43.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=-20 x_{1}\relax (t )+11 x_{2}\relax (t )+13 x_{3}\relax (t )\\ x_{2}^{\prime }\relax (t )&=12 x_{1}\relax (t )-x_{2}\relax (t )-7 x_{3}\relax (t )\\ x_{3}^{\prime }\relax (t )&=-48 x_{1}\relax (t )+21 x_{2}\relax (t )+31 x_{3}\relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.021 (sec). Leaf size: 72
dsolve([diff(x__1(t),t)=-20*x__1(t)+11*x__2(t)+13*x__3(t),diff(x__2(t),t)=12*x__1(t)-1*x__2(t)-7*x__3(t),diff(x__3(t),t)=-48*x__1(t)+21*x__2(t)+31*x__3(t)],[x__1(t), x__2(t), x__3(t)], singsol=all)
\[ x_{1}\relax (t ) = c_{1} {\mathrm e}^{4 t}+\frac {c_{2} {\mathrm e}^{8 t}}{3}+\frac {3 c_{3} {\mathrm e}^{-2 t}}{5} \] \[ x_{2}\relax (t ) = c_{1} {\mathrm e}^{4 t}-\frac {c_{2} {\mathrm e}^{8 t}}{3}-\frac {c_{3} {\mathrm e}^{-2 t}}{5} \] \[ x_{3}\relax (t ) = c_{1} {\mathrm e}^{4 t}+c_{2} {\mathrm e}^{8 t}+c_{3} {\mathrm e}^{-2 t} \]
✓ Solution by Mathematica
Time used: 0.031 (sec). Leaf size: 554
DSolve[{x1'[t]==20*x1[t]+11*x2[t]+13*x3[t],x2'[t]==12*x1[t]-1*x2[t]-7*x3[t],x3'[t]==-48*x1[t]+21*x2[t]+31*x3[t]},{x1[t],x2[t],x3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to c_2 \text {RootSum}\left [\text {$\#$1}^3-50 \text {$\#$1}^2+1208 \text {$\#$1}-4576\&,\frac {11 \text {$\#$1} e^{\text {$\#$1} t}-68 e^{\text {$\#$1} t}}{3 \text {$\#$1}^2-100 \text {$\#$1}+1208}\&\right ]+c_3 \text {RootSum}\left [\text {$\#$1}^3-50 \text {$\#$1}^2+1208 \text {$\#$1}-4576\&,\frac {13 \text {$\#$1} e^{\text {$\#$1} t}-64 e^{\text {$\#$1} t}}{3 \text {$\#$1}^2-100 \text {$\#$1}+1208}\&\right ]+c_1 \text {RootSum}\left [\text {$\#$1}^3-50 \text {$\#$1}^2+1208 \text {$\#$1}-4576\&,\frac {\text {$\#$1}^2 e^{\text {$\#$1} t}-30 \text {$\#$1} e^{\text {$\#$1} t}+116 e^{\text {$\#$1} t}}{3 \text {$\#$1}^2-100 \text {$\#$1}+1208}\&\right ] \\ \text {x2}(t)\to 12 c_1 \text {RootSum}\left [\text {$\#$1}^3-50 \text {$\#$1}^2+1208 \text {$\#$1}-4576\&,\frac {\text {$\#$1} e^{\text {$\#$1} t}-3 e^{\text {$\#$1} t}}{3 \text {$\#$1}^2-100 \text {$\#$1}+1208}\&\right ]-c_3 \text {RootSum}\left [\text {$\#$1}^3-50 \text {$\#$1}^2+1208 \text {$\#$1}-4576\&,\frac {7 \text {$\#$1} e^{\text {$\#$1} t}-296 e^{\text {$\#$1} t}}{3 \text {$\#$1}^2-100 \text {$\#$1}+1208}\&\right ]+c_2 \text {RootSum}\left [\text {$\#$1}^3-50 \text {$\#$1}^2+1208 \text {$\#$1}-4576\&,\frac {\text {$\#$1}^2 e^{\text {$\#$1} t}-51 \text {$\#$1} e^{\text {$\#$1} t}+1244 e^{\text {$\#$1} t}}{3 \text {$\#$1}^2-100 \text {$\#$1}+1208}\&\right ] \\ \text {x3}(t)\to -12 c_1 \text {RootSum}\left [\text {$\#$1}^3-50 \text {$\#$1}^2+1208 \text {$\#$1}-4576\&,\frac {4 \text {$\#$1} e^{\text {$\#$1} t}-17 e^{\text {$\#$1} t}}{3 \text {$\#$1}^2-100 \text {$\#$1}+1208}\&\right ]+3 c_2 \text {RootSum}\left [\text {$\#$1}^3-50 \text {$\#$1}^2+1208 \text {$\#$1}-4576\&,\frac {7 \text {$\#$1} e^{\text {$\#$1} t}-316 e^{\text {$\#$1} t}}{3 \text {$\#$1}^2-100 \text {$\#$1}+1208}\&\right ]+c_3 \text {RootSum}\left [\text {$\#$1}^3-50 \text {$\#$1}^2+1208 \text {$\#$1}-4576\&,\frac {\text {$\#$1}^2 e^{\text {$\#$1} t}-19 \text {$\#$1} e^{\text {$\#$1} t}-152 e^{\text {$\#$1} t}}{3 \text {$\#$1}^2-100 \text {$\#$1}+1208}\&\right ] \\ \end{align*}