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 }\relax (t )&=-y_{1}\relax (t )-4 y_{2}\relax (t )\\ y_{2}^{\prime }\relax (t )&=-y_{1}\relax (t )-y_{2}\relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.03 (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)],[y__1(t), y__2(t)], singsol=all)
\[ y_{1}\relax (t ) = 2 c_{1} {\mathrm e}^{-3 t}-2 c_{2} {\mathrm e}^{t} \] \[ y_{2}\relax (t ) = c_{1} {\mathrm e}^{-3 t}+c_{2} {\mathrm e}^{t} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 56
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 e^{-t} (c_1 \cosh (2 t)-2 c_2 \sinh (2 t)) \\ \text {y2}(t)\to \frac {1}{2} e^{-t} (2 c_2 \cosh (2 t)-c_1 \sinh (2 t)) \\ \end{align*}