12.22.7 problem section 10.5, problem 7

Internal problem ID [2260]
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
Date solved : Monday, January 27, 2025 at 05:44:14 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}y_{1} \left (t \right )&=-13 y_{1} \left (t \right )+16 y_{2} \left (t \right )\\ \frac {d}{d t}y_{2} \left (t \right )&=-9 y_{1} \left (t \right )+11 y_{2} \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.018 (sec). Leaf size: 32

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: 0.003 (sec). Leaf size: 46

DSolve[{D[ y1[t],t]==-13*y1[t]+16*y2[t],D[ y2[t],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*}