72.29.4 problem 1 (d)

Internal problem ID [19769]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 10. Systems of First Order Equations. Section 60. Critical Points and Stability for Linear Systems. Problems at page 539
Problem number : 1 (d)
Date solved : Thursday, October 02, 2025 at 04:42:07 PM
CAS classification : system_of_ODEs

\begin{align*} x^{\prime }\left (t \right )&=5 x \left (t \right )+2 y\\ y^{\prime }&=-17 x \left (t \right )-5 y \end{align*}

✓ Maple. Time used: 0.117 (sec). Leaf size: 49

ode:=[diff(x(t),t) = 5*x(t)+2*y(t), diff(y(t),t) = -17*x(t)-5*y(t)]; 
dsolve(ode);
 

\begin{align*} x \left (t \right ) &= c_1 \sin \left (3 t \right )+c_2 \cos \left (3 t \right ) \\ y \left (t \right ) &= \frac {3 c_1 \cos \left (3 t \right )}{2}-\frac {3 c_2 \sin \left (3 t \right )}{2}-\frac {5 c_1 \sin \left (3 t \right )}{2}-\frac {5 c_2 \cos \left (3 t \right )}{2} \\ \end{align*}

✓ Mathematica. Time used: 0.005 (sec). Leaf size: 58

ode={D[x[t],t]==5*x[t]+2*y[t],D[y[t],t]==-17*x[t]-5*y[t]}; 
ic={}; 
DSolve[{ode,ic},{x[t],y[t]},t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to c_1 \cos (3 t)+\frac {1}{3} (5 c_1+2 c_2) \sin (3 t)\\ y(t)&\to c_2 \cos (3 t)-\frac {1}{3} (17 c_1+5 c_2) \sin (3 t) \end{align*}

✓ Sympy. Time used: 0.053 (sec). Leaf size: 48

from sympy import * 
t = symbols("t") 
x = Function("x") 
y = Function("y") 
ode=[Eq(-5*x(t) - 2*y(t) + Derivative(x(t), t),0),Eq(17*x(t) + 5*y(t) + Derivative(y(t), t),0)] 
ics = {} 
dsolve(ode,func=[x(t),y(t)],ics=ics)
 

\[ \left [ x{\left (t \right )} = \left (\frac {3 C_{1}}{17} + \frac {5 C_{2}}{17}\right ) \sin {\left (3 t \right )} - \left (\frac {5 C_{1}}{17} - \frac {3 C_{2}}{17}\right ) \cos {\left (3 t \right )}, \ y{\left (t \right )} = C_{1} \cos {\left (3 t \right )} - C_{2} \sin {\left (3 t \right )}\right ] \]