12.22.6 problem section 10.5, problem 6

Internal problem ID [2259]
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 6
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 )&=-10 y_{1} \left (t \right )+9 y_{2} \left (t \right )\\ \frac {d}{d t}y_{2} \left (t \right )&=-4 y_{1} \left (t \right )+2 y_{2} \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.023 (sec). Leaf size: 32

dsolve([diff(y__1(t),t)=-10*y__1(t)+9*y__2(t),diff(y__2(t),t)=-4*y__1(t)+2*y__2(t)],singsol=all)
 

\begin{align*} y_{1} \left (t \right ) &= {\mathrm e}^{-4 t} \left (c_2 t +c_1 \right ) \\ y_{2} \left (t \right ) &= \frac {{\mathrm e}^{-4 t} \left (6 c_2 t +6 c_1 +c_2 \right )}{9} \\ \end{align*}

✓ Solution by Mathematica

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

DSolve[{D[ y1[t],t]==-10*y1[t]+9*y2[t],D[ y2[t],t]==-4*y1[t]+2*y2[t]},{y1[t],y2[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} \text {y1}(t)\to e^{-4 t} (-6 c_1 t+9 c_2 t+c_1) \\ \text {y2}(t)\to e^{-4 t} (-4 c_1 t+6 c_2 t+c_2) \\ \end{align*}