Internal problem ID [1838]
Book: Differential equations and their applications, 4th ed., M. Braun
Section: Section 3.9, Systems of differential equations. Complex roots. Page 344
Problem number: 3.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\left (t \right )&=x_{1} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=3 x_{1} \left (t \right )+x_{2} \left (t \right )-2 x_{3} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )+2 x_{2} \left (t \right )+x_{3} \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.046 (sec). Leaf size: 70
dsolve([diff(x__1(t),t)=1*x__1(t)-0*x__2(t)+0*x__3(t),diff(x__2(t),t)=3*x__1(t)+1*x__2(t)-2*x__3(t),diff(x__3(t),t)=2*x__1(t)+2*x__2(t)+1*x__3(t)],singsol=all)
\begin{align*} x_{1} \left (t \right ) &= c_{3} {\mathrm e}^{t} \\ x_{2} \left (t \right ) &= {\mathrm e}^{t} \left (c_{2} \sin \left (2 t \right )+c_{1} \cos \left (2 t \right )-c_{3} \cos \left (2 t \right )-c_{3} \right ) \\ x_{3} \left (t \right ) &= \frac {{\mathrm e}^{t} \left (2 c_{1} \sin \left (2 t \right )-2 c_{3} \sin \left (2 t \right )-2 c_{2} \cos \left (2 t \right )+3 c_{3} \right )}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 91
DSolve[{x1'[t]==1*x1[t]-0*x2[t]+0*x3[t],x2'[t]==3*x1[t]+1*x2[t]-2*x3[t],x3'[t]==2*x1[t]+2*x2[t]+1*x3[t]},{x1[t],x2[t],x3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to c_1 e^t \\ \text {x2}(t)\to \frac {1}{2} e^t (2 (c_1+c_2) \cos (2 t)+(3 c_1-2 c_3) \sin (2 t)-2 c_1) \\ \text {x3}(t)\to \frac {1}{2} e^t ((2 c_3-3 c_1) \cos (2 t)+2 (c_1+c_2) \sin (2 t)+3 c_1) \\ \end{align*}