Internal problem ID [1637]
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 2.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} y_{1}^{\prime }\relax (t )&=-11 y_{1}\relax (t )+4 y_{2}\relax (t )\\ y_{2}^{\prime }\relax (t )&=-26 y_{1}\relax (t )+9 y_{2}\relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.323 (sec). Leaf size: 60
dsolve([diff(y__1(t),t)=-11*y__1(t)+4*y__2(t),diff(y__2(t),t)=-26*y__1(t)+9*y__2(t)],[y__1(t), y__2(t)], singsol=all)
\[ y_{1}\relax (t ) = \frac {{\mathrm e}^{-t} \left (5 c_{1} \sin \left (2 t \right )+c_{2} \sin \left (2 t \right )-c_{1} \cos \left (2 t \right )+5 c_{2} \cos \left (2 t \right )\right )}{13} \] \[ y_{2}\relax (t ) = {\mathrm e}^{-t} \left (c_{1} \sin \left (2 t \right )+c_{2} \cos \left (2 t \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 64
DSolve[{y1'[t]==-11*y1[t]+4*y2[t],y2'[t]==-26*y1[t]+9*y2[t]},{y1[t],y2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {y1}(t)\to e^{-t} (c_1 \cos (2 t)+(2 c_2-5 c_1) \sin (2 t)) \\ \text {y2}(t)\to e^{-t} (c_2 \cos (2 t)+(5 c_2-13 c_1) \sin (2 t)) \\ \end{align*}