Internal problem ID [1833]
Book: Differential equations and their applications, 4th ed., M. Braun
Section: Section 3.8, Systems of differential equations. The eigenva1ue-eigenvector method. Page
339
Problem number: 10.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=x_{1} \relax (t )-x_{2} \relax (t )\\ x_{2}^{\prime }\relax (t )&=x_{1} \relax (t )+2 x_{2} \relax (t )+x_{3} \relax (t )\\ x_{3}^{\prime }\relax (t )&=x_{1} \relax (t )+10 x_{2} \relax (t )+2 x_{3} \relax (t ) \end {align*}
With initial conditions \[ [x_{1} \relax (0) = -1, x_{2} \relax (0) = -4, x_{3} \relax (0) = 13] \]
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 37
dsolve([diff(x__1(t),t) = x__1(t)-x__2(t), diff(x__2(t),t) = x__1(t)+2*x__2(t)+x__3(t), diff(x__3(t),t) = x__1(t)+10*x__2(t)+2*x__3(t), x__1(0) = -1, x__2(0) = -4, x__3(0) = 13],[x__1(t), x__2(t), x__3(t)], singsol=all)
\[ x_{1} \relax (t ) = -2 \,{\mathrm e}^{-t}+{\mathrm e}^{t} \] \[ x_{2} \relax (t ) = -4 \,{\mathrm e}^{-t} \] \[ x_{3} \relax (t ) = 14 \,{\mathrm e}^{-t}-{\mathrm e}^{t} \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 36
DSolve[{x1'[t]==1*x1[t]-1*x2[t]-0*x3[t],x2'[t]==1*x1[t]+2*x2[t]+1*x3[t],x3'[t]==1*x1[t]+10*x2[t]+2*x3[t]},{x1[0]==-1,x2[0]==-4,x3[0]==13},{x1[t],x2[t],x3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to 3 \sinh (t)-\cosh (t) \\ \text {x2}(t)\to -4 e^{-t} \\ \text {x3}(t)\to 13 \cosh (t)-15 \sinh (t) \\ \end{align*}