48.5.13 problem Problem 5.15 part 1

Internal problem ID [7578]
Book : THEORY OF DIFFERENTIAL EQUATIONS IN ENGINEERING AND MECHANICS. K.T. CHAU, CRC Press. Boca Raton, FL. 2018
Section : Chapter 5. Systems of First Order Differential Equations. Section 5.11 Problems. Page 360
Problem number : Problem 5.15 part 1
Date solved : Monday, January 27, 2025 at 03:06:31 PM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x_{1} \left (t \right )&=x_{1} \left (t \right )+x_{2} \left (t \right )-8\\ \frac {d}{d t}x_{2} \left (t \right )&=x_{1} \left (t \right )+x_{2} \left (t \right )+3 \end{align*}

✓ Solution by Maple

Time used: 0.028 (sec). Leaf size: 34

dsolve([diff(x__1(t),t)=x__1(t)+x__2(t)-8,diff(x__2(t),t)=x__1(t)+x__2(t)+3],singsol=all)
 

\begin{align*} x_{1} \left (t \right ) &= \frac {c_{1} {\mathrm e}^{2 t}}{2}-\frac {11 t}{2}+c_{2} \\ x_{2} \left (t \right ) &= \frac {c_{1} {\mathrm e}^{2 t}}{2}+\frac {5}{2}+\frac {11 t}{2}-c_{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 74

DSolve[{D[ x1[t],t]==x1[t]+x2[t]-8,D[ x2[t],t]==x1[t]+x2[t]+3},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} \text {x1}(t)\to \frac {1}{4} \left (-22 t+2 c_1 \left (e^{2 t}+1\right )+2 c_2 e^{2 t}+5-2 c_2\right ) \\ \text {x2}(t)\to \frac {1}{4} \left (22 t+2 c_1 \left (e^{2 t}-1\right )+2 c_2 e^{2 t}+5+2 c_2\right ) \\ \end{align*}