Internal problem ID [1610]
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 7.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} y_{1}^{\prime }\left (t \right )&=-13 y_{1} \left (t \right )+16 y_{2} \left (t \right )\\ y_{2}^{\prime }\left (t \right )&=-9 y_{1} \left (t \right )+11 y_{2} \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 33
dsolve([diff(y__1(t),t)=-13*y__1(t)+16*y__2(t),diff(y__2(t),t)=-9*y__1(t)+11*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 ) &= \frac {{\mathrm e}^{-t} \left (12 c_{2} t +12 c_{1} +c_{2} \right )}{16} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 46
DSolve[{y1'[t]==-13*y1[t]+16*y2[t],y2'[t]==-9*y1[t]+11*y2[t]},{y1[t],y2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {y1}(t)\to e^{-t} (-12 c_1 t+16 c_2 t+c_1) \\ \text {y2}(t)\to e^{-t} (-9 c_1 t+12 c_2 t+c_2) \\ \end{align*}