20.20.26 problem 26

Internal problem ID [3916]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 9, First order linear systems. Section 9.11 (Chapter review), page 665
Problem number : 26
Date solved : Monday, January 27, 2025 at 08:04:29 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x_{1} \left (t \right )&=9 x_{1} \left (t \right )-2 x_{2} \left (t \right )+9 t\\ \frac {d}{d t}x_{2} \left (t \right )&=5 x_{1} \left (t \right )-2 x_{2} \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.032 (sec). Leaf size: 43

dsolve([diff(x__1(t),t)=9*x__1(t)-2*x__2(t)+9*t,diff(x__2(t),t)=5*x__1(t)-2*x__2(t)],singsol=all)
 

\begin{align*} x_{1} \left (t \right ) &= c_{2} {\mathrm e}^{8 t}+{\mathrm e}^{-t} c_{1} -\frac {9 t}{4}+\frac {27}{32} \\ x_{2} \left (t \right ) &= \frac {c_{2} {\mathrm e}^{8 t}}{2}+5 \,{\mathrm e}^{-t} c_{1} +\frac {315}{64}-\frac {45 t}{8} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.277 (sec). Leaf size: 94

DSolve[{D[x1[t],t]==9*x1[t]-2*x2[t]+9*t,D[x2[t],t]==5*x1[t]-2*x2[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} \text {x1}(t)\to -\frac {9 t}{4}-\frac {1}{9} (c_1-2 c_2) e^{-t}+\frac {2}{9} (5 c_1-c_2) e^{8 t}+\frac {27}{32} \\ \text {x2}(t)\to -\frac {45 t}{8}-\frac {5}{9} (c_1-2 c_2) e^{-t}+\frac {1}{9} (5 c_1-c_2) e^{8 t}+\frac {315}{64} \\ \end{align*}