Internal problem ID [1616]
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 13.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} y_{1}^{\prime }\relax (t )&=-11 y_{1} \relax (t )+8 y_{2} \relax (t )\\ y_{2}^{\prime }\relax (t )&=-2 y_{1} \relax (t )-3 y_{2} \relax (t ) \end {align*}
With initial conditions \[ [y_{1} \relax (0) = 6, y_{2} \relax (0) = 2] \]
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 29
dsolve([diff(y__1(t),t) = -11*y__1(t)+8*y__2(t), diff(y__2(t),t) = -2*y__1(t)-3*y__2(t), y__1(0) = 6, y__2(0) = 2],[y__1(t), y__2(t)], singsol=all)
\[ y_{1} \relax (t ) = \frac {{\mathrm e}^{-7 t} \left (-16 t +12\right )}{2} \] \[ y_{2} \relax (t ) = {\mathrm e}^{-7 t} \left (-4 t +2\right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 30
DSolve[{y1'[t]==-11*y1[t]+8*y2[t],y2'[t]==-2*y1[t]-3*y2[t]},{y1[0]==6,y2[0]==2},{y1[t],y2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {y1}(t)\to e^{-7 t} (6-8 t) \\ \text {y2}(t)\to e^{-7 t} (2-4 t) \\ \end{align*}