Internal problem ID [1845]
Book: Differential equations and their applications, 4th ed., M. Braun
Section: Section 3.10, Systems of differential equations. Equal roots. Page 352
Problem number: Example 2, page 349.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=2 x_{1}\relax (t )+x_{2}\relax (t )+3 x_{3}\relax (t )\\ x_{2}^{\prime }\relax (t )&=2 x_{2}\relax (t )-x_{3}\relax (t )\\ x_{3}^{\prime }\relax (t )&=2 x_{3}\relax (t ) \end {align*}
With initial conditions \[ [x_{1}\relax (0) = 1, x_{2}\relax (0) = 2, x_{3}\relax (0) = 1] \]
✓ Solution by Maple
Time used: 0.084 (sec). Leaf size: 41
dsolve([diff(x__1(t),t) = 2*x__1(t)+x__2(t)+3*x__3(t), diff(x__2(t),t) = 2*x__2(t)-x__3(t), diff(x__3(t),t) = 2*x__3(t), x__1(0) = 1, x__2(0) = 2, x__3(0) = 1],[x__1(t), x__2(t), x__3(t)], singsol=all)
\[ x_{1}\relax (t ) = \frac {\left (-t^{2}+10 t +2\right ) {\mathrm e}^{2 t}}{2} \] \[ x_{2}\relax (t ) = \left (2-t \right ) {\mathrm e}^{2 t} \] \[ x_{3}\relax (t ) = {\mathrm e}^{2 t} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 42
DSolve[{x1'[t]==2*x1[t]+1*x2[t]+3*x3[t],x2'[t]==0*x1[t]+2*x2[t]-1*x3[t],x3'[t]==0*x1[t]-0*x2[t]+2*x3[t]},{x1[0]==1,x2[0]==2,x3[0]==1},{x1[t],x2[t],x3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to -\frac {1}{2} e^{2 t} ((t-10) t-2) \\ \text {x2}(t)\to -e^{2 t} (t-2) \\ \text {x3}(t)\to e^{2 t} \\ \end{align*}