58.16.4 problem 4

Internal problem ID [14888]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 7, Systems of linear differential equations. Section 7.1. Exercises page 277
Problem number : 4
Date solved : Thursday, October 02, 2025 at 09:56:14 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )+\frac {d}{d t}y \left (t \right )-x \left (t \right )-2 y \left (t \right )&=2 \,{\mathrm e}^{t}\\ \frac {d}{d t}x \left (t \right )+\frac {d}{d t}y \left (t \right )-3 x \left (t \right )-4 y \left (t \right )&={\mathrm e}^{2 t} \end{align*}

✓ Maple. Time used: 0.118 (sec). Leaf size: 22

ode:=[diff(x(t),t)+diff(y(t),t)-x(t)-2*y(t) = 2*exp(t), diff(x(t),t)+diff(y(t),t)-3*x(t)-4*y(t) = exp(2*t)]; 
dsolve(ode);
 

\begin{align*} x \left (t \right ) &= 3 \,{\mathrm e}^{t} \\ y \left (t \right ) &= -\frac {{\mathrm e}^{2 t}}{2}-2 \,{\mathrm e}^{t} \\ \end{align*}

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 25

ode={D[x[t],t]+D[y[t],t]-x[t]-2*y[t]==2*Exp[t],D[x[t],t]+D[y[t],t]-3*x[t]-4*y[t]==Exp[2*t]}; 
ic={}; 
DSolve[{ode,ic},{x[t],y[t]},t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to 3 e^t\\ y(t)&\to -\frac {1}{2} e^t \left (e^t+4\right ) \end{align*}

✗ Sympy

from sympy import * 
t = symbols("t") 
x = Function("x") 
y = Function("y") 
ode=[Eq(-x(t) - 2*y(t) - 2*exp(t) + Derivative(x(t), t) + Derivative(y(t), t),0),Eq(-3*x(t) - 4*y(t) - exp(2*t) + Derivative(x(t), t) + Derivative(y(t), t),0)] 
ics = {} 
dsolve(ode,func=[x(t),y(t)],ics=ics)