85.83.8 problem 1 (h)

Internal problem ID [23005]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 10. Systems of differential equations and their applications. A Exercises at page 444
Problem number : 1 (h)
Date solved : Thursday, October 02, 2025 at 09:17:27 PM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )+\frac {d}{d t}y \left (t \right )+2 x \left (t \right )-y \left (t \right )&=-\sin \left (t \right )\\ \frac {d}{d t}x \left (t \right )-3 x \left (t \right )+\frac {d}{d t}y \left (t \right )+2 y \left (t \right )&=4 \cos \left (t \right ) \end{align*}

✓ Maple. Time used: 0.137 (sec). Leaf size: 34

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

\begin{align*} x \left (t \right ) &= -\frac {\cos \left (t \right )}{5}+\frac {2 \sin \left (t \right )}{5}+{\mathrm e}^{-\frac {t}{8}} c_1 \\ y \left (t \right ) &= \cos \left (t \right )+\sin \left (t \right )+\frac {5 \,{\mathrm e}^{-\frac {t}{8}} c_1}{3} \\ \end{align*}

✓ Mathematica. Time used: 0.042 (sec). Leaf size: 52

ode={D[x[t],{t,1}]+2*x[t]+D[y[t],t]-y[t]==-Sin[t],D[x[t],{t,1}]-3*x[t]+D[y[t],t]+2*y[t]==4*Cos[t]}; 
ic={}; 
DSolve[{ode,ic},{x[t],y[t]},t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to \frac {2 \sin (t)}{5}-\frac {\cos (t)}{5}+\frac {8}{27} c_1 e^{-t/8}\\ y(t)&\to \sin (t)+\cos (t)+\frac {40}{81} c_1 e^{-t/8} \end{align*}

✗ Sympy

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