Internal problem ID [1595]
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 7.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} y_{1}^{\prime }\relax (t )&=-6 y_{1} \relax (t )-3 y_{2} \relax (t )\\ y_{2}^{\prime }\relax (t )&=y_{1} \relax (t )-2 y_{2} \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 36
dsolve([diff(y__1(t),t)=-6*y__1(t)-3*y__2(t),diff(y__2(t),t)=1*y__1(t)-2*y__2(t)],[y__1(t), y__2(t)], singsol=all)
\[ y_{1} \relax (t ) = -3 \,{\mathrm e}^{-5 t} c_{1}-c_{2} {\mathrm e}^{-3 t} \] \[ y_{2} \relax (t ) = {\mathrm e}^{-5 t} c_{1}+c_{2} {\mathrm e}^{-3 t} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 61
DSolve[{y1'[t]==-6*y1[t]-3*y2[t],y2'[t]==1*y1[t]-2*y2[t]},{y1[t],y2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {y1}(t)\to \frac {1}{2} e^{-5 t} \left (3 (c_1+c_2)-(c_1+3 c_2) e^{2 t}\right ) \\ \text {y2}(t)\to e^{-4 t} (c_2 \cosh (t)+(c_1+2 c_2) \sinh (t)) \\ \end{align*}