85.88.6 problem 1 (f)

Internal problem ID [23033]
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 (f)
Date solved : Thursday, October 02, 2025 at 09:17:39 PM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )+4 x \left (t \right )+3 \frac {d}{d t}y \left (t \right )+4 y \left (t \right )&=0\\ \frac {d}{d t}x \left (t \right )+2 x \left (t \right )+2 \frac {d}{d t}y \left (t \right )+2 y \left (t \right )&=0 \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&=-1 \\ y \left (0\right )&=6 \\ \end{align*}

✓ Maple. Time used: 0.029 (sec). Leaf size: 17

ode:=[diff(x(t),t)+4*x(t)+3*diff(y(t),t)+4*y(t) = 0, diff(x(t),t)+2*x(t)+2*diff(y(t),t)+2*y(t) = 0]; 
ic:=[x(0) = -1, y(0) = 6]; 
dsolve([ode,op(ic)]);
 

\begin{align*} x \left (t \right ) &= 10 t -1 \\ y \left (t \right ) &= 6-10 t \\ \end{align*}

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 18

ode={D[x[t],{t,1}]+4*x[t]+3*D[y[t],t]+4*y[t]==0, D[x[t],t]+2*x[t]+ 2*D[y[t],{t,1}]+2*y[t]==0}; 
ic={x[0]==-1,y[0]==6}; 
DSolve[{ode,ic},{x[t],y[t]},t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to 10 t-1\\ y(t)&\to 6-10 t \end{align*}

✓ Sympy. Time used: 0.060 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
x = Function("x") 
y = Function("y") 
ode=[Eq(4*x(t) + 4*y(t) + Derivative(x(t), t) + 3*Derivative(y(t), t),0),Eq(2*x(t) + 2*y(t) + Derivative(x(t), t) + 2*Derivative(y(t), t),0)] 
ics = {x(0): -1, y(0): 6} 
dsolve(ode,func=[x(t),y(t)],ics=ics)
 

\[ \left [ x{\left (t \right )} = 10 t - 1, \ y{\left (t \right )} = 6 - 10 t\right ] \]