Internal problem ID [336]
Book: Differential equations and linear algebra, 4th ed., Edwards and Penney
Section: Section 7.3, The eigenvalue method for linear systems. Page 395
Problem number: problem 22.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\left (t \right )&=3 x_{1} \left (t \right )+2 x_{2} \left (t \right )+2 x_{3} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=-5 x_{1} \left (t \right )-4 x_{2} \left (t \right )-2 x_{3} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=5 x_{1} \left (t \right )+5 x_{2} \left (t \right )+3 x_{3} \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 55
dsolve([diff(x__1(t),t)=3*x__1(t)+2*x__2(t)+2*x__3(t),diff(x__2(t),t)=-5*x__1(t)-4*x__2(t)-2*x__3(t),diff(x__3(t),t)=5*x__1(t)+5*x__2(t)+3*x__3(t)],singsol=all)
\begin{align*} x_{1} \left (t \right ) &= c_{2} {\mathrm e}^{3 t}+c_{3} {\mathrm e}^{t} \\ x_{2} \left (t \right ) &= -c_{2} {\mathrm e}^{3 t}-c_{3} {\mathrm e}^{t}+c_{1} {\mathrm e}^{-2 t} \\ x_{3} \left (t \right ) &= c_{2} {\mathrm e}^{3 t}-c_{1} {\mathrm e}^{-2 t} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 123
DSolve[{x1'[t]==3*x1[t]+2*x2[t]+2*x3[t],x2'[t]==-5*x1[t]-4*x2[t]-2*x3[t],x3'[t]==5*x1[t]+5*x2[t]+3*x3[t]},{x1[t],x2[t],x3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to e^t \left ((c_1+c_2+c_3) e^{2 t}-c_2-c_3\right ) \\ \text {x2}(t)\to e^{-2 t} \left (-\left (c_1 \left (e^{5 t}-1\right )\right )+c_2 \left (e^{3 t}-e^{5 t}+1\right )-c_3 e^{3 t} \left (e^{2 t}-1\right )\right ) \\ \text {x3}(t)\to e^{-2 t} \left (c_1 \left (e^{5 t}-1\right )+c_2 \left (e^{5 t}-1\right )+c_3 e^{5 t}\right ) \\ \end{align*}