46.11.1 problem 1

Internal problem ID [9719]
Book : DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL, WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th edition.
Section : CHAPTER 8 SYSTEMS OF LINEAR FIRST-ORDER DIFFERENTIAL EQUATIONS. EXERCISES 8.3. Page 354
Problem number : 1
Date solved : Tuesday, September 30, 2025 at 06:32:19 PM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=2 x \left (t \right )+3 y \left (t \right )-7\\ \frac {d}{d t}y \left (t \right )&=-x \left (t \right )-2 y \left (t \right )+5 \end{align*}

✓ Maple. Time used: 0.130 (sec). Leaf size: 33

ode:=[diff(x(t),t) = 2*x(t)+3*y(t)-7, diff(y(t),t) = -x(t)-2*y(t)+5]; 
dsolve(ode);
 

\begin{align*} x \left (t \right ) &= {\mathrm e}^{t} c_2 +{\mathrm e}^{-t} c_1 -1 \\ y \left (t \right ) &= -\frac {{\mathrm e}^{t} c_2}{3}-{\mathrm e}^{-t} c_1 +3 \\ \end{align*}

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 76

ode={D[x[t],t]==2*x[t]+3*y[t]-7,D[y[t],t]==-x[t]-2*y[t]+5}; 
ic={}; 
DSolve[{ode,ic},{x[t],y[t]},t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to \frac {1}{2} e^{-t} \left (-2 e^t+3 (c_1+c_2) e^{2 t}-c_1-3 c_2\right )\\ y(t)&\to \frac {1}{2} e^{-t} \left (6 e^t-(c_1+c_2) e^{2 t}+c_1+3 c_2\right ) \end{align*}

✓ Sympy. Time used: 0.086 (sec). Leaf size: 31

from sympy import * 
t = symbols("t") 
x = Function("x") 
y = Function("y") 
ode=[Eq(-2*x(t) - 3*y(t) + Derivative(x(t), t) + 7,0),Eq(x(t) + 2*y(t) + Derivative(y(t), t) - 5,0)] 
ics = {} 
dsolve(ode,func=[x(t),y(t)],ics=ics)
 

\[ \left [ x{\left (t \right )} = - C_{1} e^{- t} - 3 C_{2} e^{t} - 1, \ y{\left (t \right )} = C_{1} e^{- t} + C_{2} e^{t} + 3\right ] \]