Internal problem ID [1606]
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 3.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} y_{1}^{\prime }\relax (t )&=-7 y_{1} \relax (t )+4 y_{2} \relax (t )\\ y_{2}^{\prime }\relax (t )&=-y_{1} \relax (t )-11 y_{2} \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 33
dsolve([diff(y__1(t),t)=-7*y__1(t)+4*y__2(t),diff(y__2(t),t)=-1*y__1(t)-11*y__2(t)],[y__1(t), y__2(t)], singsol=all)
\[ y_{1} \relax (t ) = -{\mathrm e}^{-9 t} \left (2 c_{2} t +2 c_{1}+c_{2}\right ) \] \[ y_{2} \relax (t ) = {\mathrm e}^{-9 t} \left (c_{2} t +c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 46
DSolve[{y1'[t]==-7*y1[t]+4*y2[t],y2'[t]==-1*y1[t]-11*y2[t]},{y1[t],y2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {y1}(t)\to e^{-9 t} (2 c_1 t+4 c_2 t+c_1) \\ \text {y2}(t)\to e^{-9 t} (c_2-(c_1+2 c_2) t) \\ \end{align*}