Internal problem ID [381]
Book: Differential equations and linear algebra, 4th ed., Edwards and Penney
Section: Section 7.6, Multiple Eigenvalue Solutions. Page 451
Problem number: problem 24.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=28 x_{1} \relax (t )+50 x_{2} \relax (t )+100 x_{3} \relax (t )\\ x_{2}^{\prime }\relax (t )&=15 x_{1} \relax (t )+33 x_{2} \relax (t )+60 x_{3} \relax (t )\\ x_{3}^{\prime }\relax (t )&=-15 x_{1} \relax (t )-30 x_{2} \relax (t )-57 x_{3} \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 67
dsolve([diff(x__1(t),t)=28*x__1(t)+50*x__2(t)+100*x__3(t),diff(x__2(t),t)=15*x__1(t)+33*x__2(t)+60*x__3(t),diff(x__3(t),t)=-15*x__1(t)-30*x__2(t)-57*x__3(t)],[x__1(t), x__2(t), x__3(t)], singsol=all)
\[ x_{1} \relax (t ) = -\frac {5 \,{\mathrm e}^{-2 t} c_{2}}{3}-2 c_{3} {\mathrm e}^{3 t}-2 c_{1} {\mathrm e}^{3 t} \] \[ x_{2} \relax (t ) = -{\mathrm e}^{-2 t} c_{2}-c_{3} {\mathrm e}^{3 t}+c_{1} {\mathrm e}^{3 t} \] \[ x_{3} \relax (t ) = {\mathrm e}^{-2 t} c_{2}+c_{3} {\mathrm e}^{3 t} \]
✓ Solution by Mathematica
Time used: 0.051 (sec). Leaf size: 229
DSolve[{x1'[t]==28*x1[t]+50*x2[t]+100*x3[t],x2'[t]==15*x1[t]+33*x2[t]+60*x3[t],x3'[t]==-15*x1[t]-40*x2[t]-57*x3[t]},{x1[t],x2[t],x3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to \frac {1}{57} e^{t/2} \left (19 (3 c_1-5 c_2) e^{5 t/2}+95 c_2 \cos \left (\frac {5 \sqrt {95} t}{2}\right )+\sqrt {95} (6 c_1+13 c_2+24 c_3) \sin \left (\frac {5 \sqrt {95} t}{2}\right )\right ) \\ \text {x2}(t)\to \frac {1}{95} e^{t/2} \left (95 c_2 \cos \left (\frac {5 \sqrt {95} t}{2}\right )+\sqrt {95} (6 c_1+13 c_2+24 c_3) \sin \left (\frac {5 \sqrt {95} t}{2}\right )\right ) \\ \text {x3}(t)\to -\frac {e^{t/2} \left (95 (3 c_1-5 c_2) e^{5 t/2}-95 (3 c_1-5 c_2+12 c_3) \cos \left (\frac {5 \sqrt {95} t}{2}\right )+\sqrt {95} (69 c_1+197 c_2+276 c_3) \sin \left (\frac {5 \sqrt {95} t}{2}\right )\right )}{1140} \\ \end{align*}