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 }\relax (t )&=3 x_{1} \relax (t )+2 x_{2} \relax (t )+2 x_{3} \relax (t )\\ x_{2}^{\prime }\relax (t )&=-5 x_{1} \relax (t )-4 x_{2} \relax (t )-2 x_{3} \relax (t )\\ x_{3}^{\prime }\relax (t )&=5 x_{1} \relax (t )+5 x_{2} \relax (t )+3 x_{3} \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.078 (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)],[x__1(t), x__2(t), x__3(t)], singsol=all)
\[ x_{1} \relax (t ) = c_{3} {\mathrm e}^{3 t}-c_{1} {\mathrm e}^{t} \] \[ x_{2} \relax (t ) = -{\mathrm e}^{-2 t} c_{2}-c_{3} {\mathrm e}^{3 t}+c_{1} {\mathrm e}^{t} \] \[ x_{3} \relax (t ) = {\mathrm e}^{-2 t} c_{2}+c_{3} {\mathrm e}^{3 t} \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 95
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 (c_1+c_2+c_3) e^{3 t}-(c_2+c_3) e^t \\ \text {x2}(t)\to e^{-2 t} \left (c_1 \left (-e^{5 t}\right )-2 (c_2+c_3) e^{4 t} \sinh (t)+c_1+c_2\right ) \\ \text {x3}(t)\to (c_1+c_2+c_3) e^{3 t}-(c_1+c_2) e^{-2 t} \\ \end{align*}