Internal problem ID [1852]
Book: Differential equations and their applications, 4th ed., M. Braun
Section: Section 3.10, Systems of differential equations. Equal roots. Page 352
Problem number: 7.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=x_{1}\relax (t )+2 x_{2}\relax (t )-3 x_{3}\relax (t )\\ x_{2}^{\prime }\relax (t )&=x_{1}\relax (t )+x_{2}\relax (t )+2 x_{3}\relax (t )\\ x_{3}^{\prime }\relax (t )&=x_{1}\relax (t )-x_{2}\relax (t )+4 x_{3}\relax (t ) \end {align*}
With initial conditions \[ [x_{1}\relax (0) = 1, x_{2}\relax (0) = 0, x_{3}\relax (0) = 0] \]
✓ Solution by Maple
Time used: 0.052 (sec). Leaf size: 32
dsolve([diff(x__1(t),t) = x__1(t)+2*x__2(t)-3*x__3(t), diff(x__2(t),t) = x__1(t)+x__2(t)+2*x__3(t), diff(x__3(t),t) = x__1(t)-x__2(t)+4*x__3(t), x__1(0) = 1, x__2(0) = 0, x__3(0) = 0],[x__1(t), x__2(t), x__3(t)], singsol=all)
\[ x_{1}\relax (t ) = -\left (t -1\right ) {\mathrm e}^{2 t} \] \[ x_{2}\relax (t ) = {\mathrm e}^{2 t} t \] \[ x_{3}\relax (t ) = {\mathrm e}^{2 t} t \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 35
DSolve[{x1'[t]==1*x1[t]+2*x2[t]-3*x3[t],x2'[t]==1*x1[t]+1*x2[t]+2*x3[t],x3'[t]==1*x1[t]-1*x2[t]+4*x3[t]},{x1[0]==1,x2[0]==0,x3[0]==0},{x1[t],x2[t],x3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to -e^{2 t} (t-1) \\ \text {x2}(t)\to e^{2 t} t \\ \text {x3}(t)\to e^{2 t} t \\ \end{align*}