Internal problem ID [1592]
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 4.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} y_{1}^{\prime }\left (t \right )&=-y_{1} \left (t \right )-4 y_{2} \left (t \right )\\ y_{2}^{\prime }\left (t \right )&=-y_{1} \left (t \right )-y_{2} \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 32
dsolve([diff(y__1(t),t)=-1*y__1(t)-4*y__2(t),diff(y__2(t),t)=-1*y__1(t)-1*y__2(t)],singsol=all)
\begin{align*} y_{1} \left (t \right ) &= c_{1} {\mathrm e}^{t}+c_{2} {\mathrm e}^{-3 t} \\ y_{2} \left (t \right ) &= -\frac {c_{1} {\mathrm e}^{t}}{2}+\frac {c_{2} {\mathrm e}^{-3 t}}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 71
DSolve[{y1'[t]==-1*y1[t]-4*y2[t],y2'[t]==-1*y1[t]-1*y2[t]},{y1[t],y2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {y1}(t)\to \frac {1}{2} e^{-3 t} \left (c_1 \left (e^{4 t}+1\right )-2 c_2 \left (e^{4 t}-1\right )\right ) \\ \text {y2}(t)\to \frac {1}{4} e^{-3 t} \left (2 c_2 \left (e^{4 t}+1\right )-c_1 \left (e^{4 t}-1\right )\right ) \\ \end{align*}