Internal problem ID [1593]
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 5.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} y_{1}^{\prime }\left (t \right )&=2 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: 0.031 (sec). Leaf size: 35
dsolve([diff(y__1(t),t)=2*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)
\[ y_{1} \left (t \right ) = -4 c_{1} {\mathrm e}^{3 t}+{\mathrm e}^{-2 t} c_{2} \] \[ y_{2} \left (t \right ) = c_{1} {\mathrm e}^{3 t}+{\mathrm e}^{-2 t} c_{2} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 72
DSolve[{y1'[t]==2*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}{5} e^{-2 t} \left (c_1 \left (4 e^{5 t}+1\right )-4 c_2 \left (e^{5 t}-1\right )\right ) \text {y2}(t)\to \frac {1}{5} e^{-2 t} \left (c_2 \left (e^{5 t}+4\right )-c_1 \left (e^{5 t}-1\right )\right ) \end{align*}