Internal problem ID [1634]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 10 Linear system of Differential equations. Section 10.5, constant coefficient
homogeneous system II. Page 555
Problem number: section 10.5, problem 31.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} y_{1}^{\prime }\relax (t )&=-3 y_{1}\relax (t )-3 y_{2}\relax (t )+4 y_{3}\relax (t )\\ y_{2}^{\prime }\relax (t )&=4 y_{1}\relax (t )+5 y_{2}\relax (t )-8 y_{3}\relax (t )\\ y_{3}^{\prime }\relax (t )&=2 y_{1}\relax (t )+3 y_{2}\relax (t )-5 y_{3}\relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.069 (sec). Leaf size: 55
dsolve([diff(y__1(t),t)=-3*y__1(t)-3*y__2(t)+4*y__3(t),diff(y__2(t),t)=4*y__1(t)+5*y__2(t)-8*y__3(t),diff(y__3(t),t)=2*y__1(t)+3*y__2(t)-5*y__3(t)],[y__1(t), y__2(t), y__3(t)], singsol=all)
\[ y_{1}\relax (t ) = -\frac {{\mathrm e}^{-t} \left (2 c_{3} t +3 c_{1}+2 c_{2}-c_{3}\right )}{2} \] \[ y_{2}\relax (t ) = {\mathrm e}^{-t} \left (2 c_{3} t +c_{1}+2 c_{2}\right ) \] \[ y_{3}\relax (t ) = {\mathrm e}^{-t} \left (c_{3} t +c_{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 83
DSolve[{y1'[t]==-3*y1[t]-3*y2[t]+4*y3[t],y2'[t]==4*y1[t]+5*y2[t]-8*y3[t],y3'[t]==2*y1[t]+3*y2[t]-5*y3[t]},{y1[t],y2[t],y3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {y1}(t)\to e^{-t} (-2 c_1 t-3 c_2 t+4 c_3 t+c_1) \\ \text {y2}(t)\to e^{-t} ((4 c_1+6 c_2-8 c_3) t+c_2) \\ \text {y3}(t)\to e^{-t} ((2 c_1+3 c_2-4 c_3) t+c_3) \\ \end{align*}