Internal problem ID [1605]
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 2.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} y_{1}^{\prime }\left (t \right )&=-y_{2} \left (t \right )\\ y_{2}^{\prime }\left (t \right )&=y_{1} \left (t \right )-2 y_{2} \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 31
dsolve([diff(y__1(t),t)=0*y__1(t)-1*y__2(t),diff(y__2(t),t)=1*y__1(t)-2*y__2(t)],singsol=all)
\begin{align*} y_{1} \left (t \right ) &= {\mathrm e}^{-t} \left (c_{2} t +c_{1} \right ) \\ y_{2} \left (t \right ) &= {\mathrm e}^{-t} \left (c_{2} t +c_{1} -c_{2} \right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 44
DSolve[{y1'[t]==0*y1[t]-1*y2[t],y2'[t]==1*y1[t]-2*y2[t]},{y1[t],y2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {y1}(t)\to e^{-t} (c_1 (t+1)-c_2 t) \\ \text {y2}(t)\to e^{-t} ((c_1-c_2) t+c_2) \\ \end{align*}