Internal problem ID [356]
Book: Differential equations and linear algebra, 4th ed., Edwards and Penney
Section: Section 7.6, Multiple Eigenvalue Solutions. Examples. Page 437
Problem number: Example 4.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=x_{2}\relax (t )+2 x_{3}\relax (t )\\ x_{2}^{\prime }\relax (t )&=-5 x_{1}\relax (t )-3 x_{2}\relax (t )-7 x_{3}\relax (t )\\ x_{3}^{\prime }\relax (t )&=x_{1}\relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.02 (sec). Leaf size: 75
dsolve([diff(x__1(t),t)=0*x__1(t)+1*x__2(t)+2*x__3(t),diff(x__2(t),t)=-5*x__1(t)-3*x__2(t)-7*x__3(t),diff(x__3(t),t)=1*x__1(t)+0*x__2(t)+0*x__3(t)],[x__1(t), x__2(t), x__3(t)], singsol=all)
\[ x_{1}\relax (t ) = -{\mathrm e}^{-t} \left (c_{3} t^{2}+c_{2} t -2 c_{3} t +c_{1}-c_{2}\right ) \] \[ x_{2}\relax (t ) = -{\mathrm e}^{-t} \left (c_{3} t^{2}+c_{2} t +4 c_{3} t +c_{1}+2 c_{2}-2 c_{3}\right ) \] \[ x_{3}\relax (t ) = {\mathrm e}^{-t} \left (c_{3} t^{2}+c_{2} t +c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 125
DSolve[{x1'[t]==0*x1[t]+1*x2[t]+2*x3[t],x2'[t]==-5*x1[t]-3*x2[t]-7*x3[t],x3'[t]==1*x1[t]+0*x2[t]+0*x[t]},{x1[t],x2[t],x3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to \frac {1}{2} e^{-t} \left (2 c_1 \left (-t^2+t+1\right )-c_2 (t-2) t+c_3 (4-3 t) t\right ) \\ \text {x2}(t)\to \frac {1}{2} e^{-t} (2 c_2-t (2 c_1 (t+5)+c_2 (t+4)+c_3 (3 t+14))) \\ \text {x3}(t)\to \frac {1}{2} e^{-t} (t (2 c_1 (t+1)+c_2 t)+c_3 (t (3 t+2)+2)) \\ \end{align*}