Internal problem ID [345]
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 42.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=-40 x_{1} \relax (t )-12 x_{2} \relax (t )+54 x_{3} \relax (t )\\ x_{2}^{\prime }\relax (t )&=35 x_{1} \relax (t )+13 x_{2} \relax (t )-46 x_{3} \relax (t )\\ x_{3}^{\prime }\relax (t )&=-25 x_{1} \relax (t )-7 x_{2} \relax (t )+34 x_{3} \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 59
dsolve([diff(x__1(t),t)=-40*x__1(t)-12*x__2(t)+54*x__3(t),diff(x__2(t),t)=35*x__1(t)+13*x__2(t)-46*x__3(t),diff(x__3(t),t)=-25*x__1(t)-7*x__2(t)+34*x__3(t)],[x__1(t), x__2(t), x__3(t)], singsol=all)
\[ x_{1} \relax (t ) = c_{2} {\mathrm e}^{2 t}+2 c_{3} {\mathrm e}^{5 t}+\frac {3 c_{1}}{2} \] \[ x_{2} \relax (t ) = c_{2} {\mathrm e}^{2 t}-3 c_{3} {\mathrm e}^{5 t}-\frac {c_{1}}{2} \] \[ x_{3} \relax (t ) = c_{1}+c_{2} {\mathrm e}^{2 t}+c_{3} {\mathrm e}^{5 t} \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 160
DSolve[{x1'[t]==-40*x1[t]-12*x2[t]+54*x3[t],x2'[t]==35*x1[t]+13*x2[t]-46*x3[t],x3'[t]==-25*x1[t]-7*x2[t]+34*x3[t]},{x1[t],x2[t],x3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to (5 c_1+c_2-7 c_3) \left (-e^{2 t}\right )-2 (3 c_1+c_2-4 c_3) e^{5 t}+3 (4 c_1+c_2-5 c_3) \\ \text {x2}(t)\to -(5 c_1+c_2-7 c_3) e^{2 t}+3 (3 c_1+c_2-4 c_3) e^{5 t}-4 c_1-c_2+5 c_3 \\ \text {x3}(t)\to (5 c_1+c_2-7 c_3) \left (-e^{2 t}\right )-(3 c_1+c_2-4 c_3) e^{5 t}+2 (4 c_1+c_2-5 c_3) \\ \end{align*}