85.88.2 problem 1 (b)

Internal problem ID [23029]
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 499
Problem number : 1 (b)
Date solved : Thursday, October 02, 2025 at 09:17:37 PM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )-x \left (t \right )+2 \frac {d}{d t}y \left (t \right )+7 y \left (t \right )&=0\\ 2 \frac {d}{d t}x \left (t \right )+\frac {d}{d t}y \left (t \right )+x \left (t \right )+5 y \left (t \right )&=0 \end{align*}

✓ Maple. Time used: 0.051 (sec). Leaf size: 30

ode:=[diff(x(t),t)-x(t)+2*diff(y(t),t)+7*y(t) = 0, 2*diff(x(t),t)+x(t)+diff(y(t),t)+5*y(t) = 0]; 
dsolve(ode);
 

\begin{align*} x \left (t \right ) &= {\mathrm e}^{-2 t} \left (c_2 t +c_1 \right ) \\ y \left (t \right ) &= {\mathrm e}^{-2 t} \left (c_2 t +c_1 -c_2 \right ) \\ \end{align*}

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 44

ode={D[x[t],{t,1}]-x[t]+2*D[y[t],t]+7*y[t]==0, 2*D[x[t],{t,1}]+x[t]+ D[y[t],{t,1}]+5*y[t]==0}; 
ic={}; 
DSolve[{ode,ic},{x[t],y[t]},t,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.068 (sec). Leaf size: 36

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

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