Internal problem ID [335]
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 21.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=5 x_{1} \relax (t )-6 x_{3} \relax (t )\\ x_{2}^{\prime }\relax (t )&=2 x_{1} \relax (t )-x_{2} \relax (t )-2 x_{3} \relax (t )\\ x_{3}^{\prime }\relax (t )&=4 x_{1} \relax (t )-2 x_{2} \relax (t )-4 x_{3} \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 54
dsolve([diff(x__1(t),t)=5*x__1(t)+0*x__2(t)-6*x__3(t),diff(x__2(t),t)=2*x__1(t)-1*x__2(t)-2*x__3(t),diff(x__3(t),t)=4*x__1(t)-2*x__2(t)-4*x__3(t)],[x__1(t), x__2(t), x__3(t)], singsol=all)
\[ x_{1} \relax (t ) = c_{2} {\mathrm e}^{-t}+\frac {3 c_{3} {\mathrm e}^{t}}{2}+\frac {6 c_{1}}{5} \] \[ x_{2} \relax (t ) = \frac {c_{2} {\mathrm e}^{-t}}{2}+\frac {c_{3} {\mathrm e}^{t}}{2}+\frac {2 c_{1}}{5} \] \[ x_{3} \relax (t ) = c_{1}+c_{2} {\mathrm e}^{-t}+c_{3} {\mathrm e}^{t} \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 123
DSolve[{x1'[t]==5*x1[t]+0*x2[t]-6*x3[t],x2'[t]==2*x1[t]-1*x2[t]-2*x3[t],x3'[t]==4*x1[t]-2*x2[t]-4*x3[t]},{x1[t],x2[t],x3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to (c_1+12 c_2-6 c_3) \cosh (t)+(5 c_1-6 c_3) \sinh (t)+6 (c_3-2 c_2) \\ \text {x2}(t)\to 5 c_2 \cosh (t)-2 c_3 \cosh (t)-(-2 c_1+c_2+2 c_3) \sinh (t)-4 c_2+2 c_3 \\ \text {x3}(t)\to -2 (c_1-3 c_2) e^{-t}+2 (c_1+2 c_2-2 c_3) e^t+5 (c_3-2 c_2) \\ \end{align*}