Internal problem ID [384]
Book: Differential equations and linear algebra, 4th ed., Edwards and Penney
Section: Section 7.6, Multiple Eigenvalue Solutions. Page 451
Problem number: problem 27.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=-3 x_{1} \relax (t )+5 x_{2} \relax (t )-5 x_{3} \relax (t )\\ x_{2}^{\prime }\relax (t )&=3 x_{1} \relax (t )-x_{2} \relax (t )+3 x_{3} \relax (t )\\ x_{3}^{\prime }\relax (t )&=8 x_{1} \relax (t )-8 x_{2} \relax (t )+10 x_{3} \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.093 (sec). Leaf size: 56
dsolve([diff(x__1(t),t)=-3*x__1(t)+5*x__2(t)-5*x__3(t),diff(x__2(t),t)=3*x__1(t)-1*x__2(t)+3*x__3(t),diff(x__3(t),t)=8*x__1(t)-8*x__2(t)+10*x__3(t)],[x__1(t), x__2(t), x__3(t)], singsol=all)
\[ x_{1} \relax (t ) = \frac {{\mathrm e}^{2 t} \left (-5 t c_{3}+8 c_{1}-5 c_{2}+c_{3}\right )}{8} \] \[ x_{2} \relax (t ) = \frac {{\mathrm e}^{2 t} \left (3 t c_{3}+8 c_{1}+3 c_{2}\right )}{8} \] \[ x_{3} \relax (t ) = {\mathrm e}^{2 t} \left (t c_{3}+c_{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.032 (sec). Leaf size: 174
DSolve[{x1'[t]==-3*x1[t]+5*x2[t]-5*x3[t],x2'[t]==4*x1[t]-1*x2[t]+4*x3[t],x3'[t]==8*x1[t]-8*x2[t]+10*x3[t]},{x1[t],x2[t],x3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to \frac {1}{3} e^{2 t} \left (-5 (c_1+c_3) \cos \left (\sqrt {3} t\right )-5 \sqrt {3} (c_1-c_2+c_3) \sin \left (\sqrt {3} t\right )+8 c_1+5 c_3\right ) \\ \text {x2}(t)\to \frac {1}{3} e^{2 t} \left (3 c_2 \cos \left (\sqrt {3} t\right )+\sqrt {3} (4 c_1-3 c_2+4 c_3) \sin \left (\sqrt {3} t\right )\right ) \\ \text {x3}(t)\to \frac {1}{3} e^{2 t} \left (8 (c_1+c_3) \cos \left (\sqrt {3} t\right )+8 \sqrt {3} (c_1-c_2+c_3) \sin \left (\sqrt {3} t\right )-8 c_1-5 c_3\right ) \\ \end{align*}