Internal problem ID [1626]
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 23.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} y_{1}^{\prime }\relax (t )&=-5 y_{1} \relax (t )-y_{2} \relax (t )+11 y_{3} \relax (t )\\ y_{2}^{\prime }\relax (t )&=-7 y_{1} \relax (t )+y_{2} \relax (t )+13 y_{3} \relax (t )\\ y_{3}^{\prime }\relax (t )&=-4 y_{1} \relax (t )+8 y_{3} \relax (t ) \end {align*}
With initial conditions \[ [y_{1} \relax (0) = 0, y_{2} \relax (0) = 2, y_{3} \relax (0) = 2] \]
✓ Solution by Maple
Time used: 0.109 (sec). Leaf size: 44
dsolve([diff(y__1(t),t) = -5*y__1(t)-y__2(t)+11*y__3(t), diff(y__2(t),t) = -7*y__1(t)+y__2(t)+13*y__3(t), diff(y__3(t),t) = -4*y__1(t)+8*y__3(t), y__1(0) = 0, y__2(0) = 2, y__3(0) = 2],[y__1(t), y__2(t), y__3(t)], singsol=all)
\[ y_{1} \relax (t ) = -3+3 \,{\mathrm e}^{4 t}+8 t \] \[ y_{2} \relax (t ) = 6 \,{\mathrm e}^{4 t}-4+4 t \] \[ y_{3} \relax (t ) = -1+4 t +3 \,{\mathrm e}^{4 t} \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 47
DSolve[{y1'[t]==-5*y1[t]-1*y2[t]+11*y3[t],y2'[t]==-7*y1[t]+1*y2[t]+13*y3[t],y3'[t]==-4*y1[t]-0*y2[t]+8*y3[t]},{y1[0]==0,y2[0]==2,y3[0]==2},{y1[t],y2[t],y3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {y1}(t)\to 8 t+3 e^{4 t}-3 \\ \text {y2}(t)\to 4 t+6 e^{4 t}-4 \\ \text {y3}(t)\to 4 t+3 e^{4 t}-1 \\ \end{align*}