67.27.13 problem 38.10 (g)

Internal problem ID [17056]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 38. Systems of differential equations. A starting point. Additional Exercises. page 786
Problem number : 38.10 (g)
Date solved : Thursday, October 02, 2025 at 01:42:24 PM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=8 x \left (t \right )+2 y \left (t \right )-17\\ \frac {d}{d t}y \left (t \right )&=4 x \left (t \right )+y \left (t \right )-13 \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&=0 \\ y \left (0\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.163 (sec). Leaf size: 27

ode:=[diff(x(t),t) = 8*x(t)+2*y(t)-17, diff(y(t),t) = 4*x(t)+y(t)-13]; 
ic:=[x(0) = 0, y(0) = 0]; 
dsolve([ode,op(ic)]);
 

\begin{align*} x \left (t \right ) &= -2 \,{\mathrm e}^{9 t}+t +2 \\ y \left (t \right ) &= -{\mathrm e}^{9 t}+1-4 t \\ \end{align*}

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 30

ode={D[x[t],t]==8*x[t]+2*y[t]-17,D[y[t],t]==4*x[t]+y[t]-13}; 
ic={x[0]==0,y[0]==0}; 
DSolve[{ode,ic},{x[t],y[t]},t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to t-2 e^{9 t}+2\\ y(t)&\to -4 t-e^{9 t}+1 \end{align*}

✓ Sympy. Time used: 0.080 (sec). Leaf size: 32

from sympy import * 
t = symbols("t") 
x = Function("x") 
y = Function("y") 
ode=[Eq(-8*x(t) - 2*y(t) + Derivative(x(t), t) + 17,0),Eq(-4*x(t) - y(t) + Derivative(y(t), t) + 13,0)] 
ics = {} 
dsolve(ode,func=[x(t),y(t)],ics=ics)
 

\[ \left [ x{\left (t \right )} = - \frac {C_{1}}{4} + 2 C_{2} e^{9 t} + t + 2, \ y{\left (t \right )} = C_{1} + C_{2} e^{9 t} - 4 t + 1\right ] \]