12.22.3 problem section 10.5, problem 3

Internal problem ID [2256]
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 3
Date solved : Monday, January 27, 2025 at 05:44:11 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}y_{1} \left (t \right )&=-7 y_{1} \left (t \right )+4 y_{2} \left (t \right )\\ \frac {d}{d t}y_{2} \left (t \right )&=-y_{1} \left (t \right )-11 y_{2} \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.023 (sec). Leaf size: 34

dsolve([diff(y__1(t),t)=-7*y__1(t)+4*y__2(t),diff(y__2(t),t)=-1*y__1(t)-11*y__2(t)],singsol=all)
 

\begin{align*} y_{1} \left (t \right ) &= {\mathrm e}^{-9 t} \left (c_2 t +c_1 \right ) \\ y_{2} \left (t \right ) &= -\frac {{\mathrm e}^{-9 t} \left (2 c_2 t +2 c_1 -c_2 \right )}{4} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 46

DSolve[{D[ y1[t],t]==-7*y1[t]+4*y2[t],D[ y2[t],t]==-1*y1[t]-11*y2[t]},{y1[t],y2[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} \text {y1}(t)\to e^{-9 t} (2 c_1 t+4 c_2 t+c_1) \\ \text {y2}(t)\to e^{-9 t} (c_2-(c_1+2 c_2) t) \\ \end{align*}