Internal problem ID [1639]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 10 Linear system of Differential equations. Section 10.6, constant coefficient
homogeneous system III. Page 566
Problem number: section 10.6, problem 4.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} y_{1}^{\prime }\left (t \right )&=5 y_{1} \left (t \right )-6 y_{2} \left (t \right )\\ y_{2}^{\prime }\left (t \right )&=3 y_{1} \left (t \right )-y_{2} \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 58
dsolve([diff(y__1(t),t)=5*y__1(t)-6*y__2(t),diff(y__2(t),t)=3*y__1(t)-1*y__2(t)],singsol=all)
\begin{align*} y_{1} \left (t \right ) &= {\mathrm e}^{2 t} \left (c_{1} \sin \left (3 t \right )+c_{2} \cos \left (3 t \right )\right ) \\ y_{2} \left (t \right ) &= \frac {{\mathrm e}^{2 t} \left (c_{1} \sin \left (3 t \right )+c_{2} \sin \left (3 t \right )-c_{1} \cos \left (3 t \right )+c_{2} \cos \left (3 t \right )\right )}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 60
DSolve[{y1'[t]==5*y1[t]-6*y2[t],y2'[t]==3*y1[t]-1*y2[t]},{y1[t],y2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {y1}(t)\to e^{2 t} (c_1 \cos (3 t)+(c_1-2 c_2) \sin (3 t)) \\ \text {y2}(t)\to e^{2 t} (c_2 \cos (3 t)+(c_1-c_2) \sin (3 t)) \\ \end{align*}