Internal problem ID [1598]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 10 Linear system of Differential equations. Section 10.4, constant coefficient
homogeneous system. Page 540
Problem number: section 10.4, problem 10.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} y_{1}^{\prime }\relax (t )&=3 y_{1}\relax (t )+5 y_{2}\relax (t )+8 y_{3}\relax (t )\\ y_{2}^{\prime }\relax (t )&=y_{1}\relax (t )-y_{2}\relax (t )-2 y_{3}\relax (t )\\ y_{3}^{\prime }\relax (t )&=-y_{1}\relax (t )-y_{2}\relax (t )-y_{3}\relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.08 (sec). Leaf size: 61
dsolve([diff(y__1(t),t)=3*y__1(t)+5*y__2(t)+8*y__3(t),diff(y__2(t),t)=1*y__1(t)-1*y__2(t)-2*y__3(t),diff(y__3(t),t)=-1*y__1(t)-1*y__2(t)-1*y__3(t)],[y__1(t), y__2(t), y__3(t)], singsol=all)
\[ y_{1}\relax (t ) = -\frac {7 c_{2} {\mathrm e}^{2 t}}{4}-\frac {2 c_{3} {\mathrm e}^{t}}{3}-c_{1} {\mathrm e}^{-2 t} \] \[ y_{2}\relax (t ) = -\frac {4 c_{3} {\mathrm e}^{t}}{3}-\frac {5 c_{2} {\mathrm e}^{2 t}}{4}+c_{1} {\mathrm e}^{-2 t} \] \[ y_{3}\relax (t ) = c_{2} {\mathrm e}^{2 t}+c_{3} {\mathrm e}^{t} \]
✓ Solution by Mathematica
Time used: 0.028 (sec). Leaf size: 193
DSolve[{y1'[t]==3*y1[t]+5*y2[t]+8*y3[t],y2'[t]==1*y1[t]-1*y2[t]-2*y3[t],y1'[t]==-1*y1[t]-1*y2[t]-1*y3[t]},{y1[t],y2[t],y3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {y1}(t)\to \frac {e^{-t/9} \left (\sqrt {35} (2 c_2-121 c_1) \sin \left (\frac {\sqrt {35} t}{9}\right )-7 (74 c_1+53 c_2) \cos \left (\frac {\sqrt {35} t}{9}\right )\right )}{1575} \\ \text {y2}(t)\to \frac {e^{-t/9} \left (7 (901 c_1+202 c_2) \cos \left (\frac {\sqrt {35} t}{9}\right )-\sqrt {35} (34 c_1+379 c_2) \sin \left (\frac {\sqrt {35} t}{9}\right )\right )}{4725} \\ \text {y3}(t)\to \frac {e^{-t/9} \left (2 \sqrt {35} (92 c_1+125 c_2) \sin \left (\frac {\sqrt {35} t}{9}\right )-14 (251 c_1+32 c_2) \cos \left (\frac {\sqrt {35} t}{9}\right )\right )}{4725} \\ \end{align*}