87.21.5 problem 5

Internal problem ID [23719]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 3. Linear Systems. Exercise at page 178
Problem number : 5
Date solved : Thursday, October 02, 2025 at 09:44:34 PM
CAS classification : system_of_ODEs

\begin{align*} x^{\prime }&=3 x-2 y \left (t \right )\\ y^{\prime }\left (t \right )&=17 x-7 y \left (t \right ) \end{align*}

✓ Maple. Time used: 0.067 (sec). Leaf size: 60

ode:=[diff(x(t),t) = 3*x(t)-2*y(t), diff(y(t),t) = 17*x(t)-7*y(t)]; 
dsolve(ode);
 

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

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 72

ode={D[x[t],t]==3*x[t]-2*y[t],D[y[t],t]==17*x[t]-7*y[t] }; 
ic={}; 
DSolve[{ode,ic},{x[t],y[t]},t,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.105 (sec). Leaf size: 70

from sympy import * 
t = symbols("t") 
x = Function("x") 
y = Function("y") 
ode=[Eq(-3*x(t) + 2*y(t) + Derivative(x(t), t),0),Eq(-17*x(t) + 7*y(t) + Derivative(y(t), t),0)] 
ics = {} 
dsolve(ode,func=[x(t),y(t)],ics=ics)
 

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