48.5.14 problem Problem 5.15 part 3

Internal problem ID [7579]
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 3
Date solved : Sunday, March 30, 2025 at 12:15:56 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*}

With initial conditions

\begin{align*} x_{1} \left (0\right ) = 1\\ x_{2} \left (0\right ) = 2 \end{align*}

✓ Maple. Time used: 0.146 (sec). Leaf size: 29

ode:=[diff(x__1(t),t) = x__1(t)+x__2(t)-8, diff(x__2(t),t) = x__1(t)+x__2(t)+3]; 
ic:=x__1(0) = 1x__2(0) = 2; 
dsolve([ode,ic]);
 

\begin{align*} x_{1} \left (t \right ) &= \frac {{\mathrm e}^{2 t}}{4}-\frac {11 t}{2}+\frac {3}{4} \\ x_{2} \left (t \right ) &= \frac {{\mathrm e}^{2 t}}{4}+\frac {7}{4}+\frac {11 t}{2} \\ \end{align*}

✓ Mathematica. Time used: 0.006 (sec). Leaf size: 36

ode={D[ x1[t],t]==x1[t]+x2[t]-8,D[ x2[t],t]==x1[t]+x2[t]+3}; 
ic={x1[0]==1,x2[0]==2}; 
DSolve[{ode,ic},{x1[t],x2[t]},t,IncludeSingularSolutions->True]
 

\begin{align*} \text {x1}(t)\to \frac {1}{4} \left (-22 t+e^{2 t}+3\right ) \\ \text {x2}(t)\to \frac {1}{4} \left (22 t+e^{2 t}+7\right ) \\ \end{align*}

✓ Sympy. Time used: 0.181 (sec). Leaf size: 37

from sympy import * 
t = symbols("t") 
x__1 = Function("x__1") 
x__2 = Function("x__2") 
ode=[Eq(-x__1(t) - x__2(t) + Derivative(x__1(t), t) + 8,0),Eq(-x__1(t) - x__2(t) + Derivative(x__2(t), t) - 3,0)] 
ics = {} 
dsolve(ode,func=[x__1(t),x__2(t)],ics=ics)
 

\[ \left [ x^{1}{\left (t \right )} = - C_{1} + C_{2} e^{2 t} - \frac {11 t}{2} + \frac {5}{4}, \ x^{2}{\left (t \right )} = C_{1} + C_{2} e^{2 t} + \frac {11 t}{2} + \frac {5}{4}\right ] \]