12.23.2 problem section 10.6, problem 2

Internal problem ID [2287]
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
Date solved : Monday, January 27, 2025 at 05:44:37 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}y_{1} \left (t \right )&=-11 y_{1} \left (t \right )+4 y_{2} \left (t \right )\\ \frac {d}{d t}y_{2} \left (t \right )&=-26 y_{1} \left (t \right )+9 y_{2} \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.023 (sec). Leaf size: 59

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)],singsol=all)
 

\begin{align*} y_{1} \left (t \right ) &= {\mathrm e}^{-t} \left (c_1 \sin \left (2 t \right )+c_2 \cos \left (2 t \right )\right ) \\ y_{2} \left (t \right ) &= \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 )}{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.006 (sec). Leaf size: 64

DSolve[{D[ y1[t],t]==-11*y1[t]+4*y2[t],D[ y2[t],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*}