Internal problem ID [1844]
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 1, page 348.
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_{2}\relax (t )\\ x_{3}^{\prime }\relax (t )&=2 x_{3}\relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.057 (sec). Leaf size: 29
dsolve([diff(x__1(t),t)=1*x__1(t)+1*x__2(t)+0*x__3(t),diff(x__2(t),t)=0*x__1(t)+1*x__2(t)-0*x__3(t),diff(x__3(t),t)=0*x__1(t)-0*x__2(t)+2*x__3(t)],[x__1(t), x__2(t), x__3(t)], singsol=all)
\[ x_{1}\relax (t ) = \left (c_{2} t +c_{1}\right ) {\mathrm e}^{t} \] \[ x_{2}\relax (t ) = c_{2} {\mathrm e}^{t} \] \[ x_{3}\relax (t ) = c_{3} {\mathrm e}^{2 t} \]
✓ Solution by Mathematica
Time used: 0.026 (sec). Leaf size: 64
DSolve[{x1'[t]==1*x1[t]+1*x2[t]+0*x3[t],x2'[t]==0*x1[t]+1*x2[t]-0*x3[t],x3'[t]==0*x1[t]-0*x2[t]+2*x3[t]},{x1[t],x2[t],x3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to e^t (c_2 t+c_1) \\ \text {x2}(t)\to c_2 e^t \\ \text {x3}(t)\to c_3 e^{2 t} \\ \text {x1}(t)\to e^t (c_2 t+c_1) \\ \text {x2}(t)\to c_2 e^t \\ \text {x3}(t)\to 0 \\ \end{align*}