82.8.22 problem 36-23

Internal problem ID [21893]
Book : The Differential Equations Problem Solver. VOL. II. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 36. Nonlinear differential equations. Page 1203
Problem number : 36-23
Date solved : Thursday, October 02, 2025 at 08:05:49 PM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=2 x \left (t \right )-7 y \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=3 x \left (t \right )-8 y \left (t \right ) \end{align*}

✓ Maple. Time used: 0.041 (sec). Leaf size: 34

ode:=[diff(x(t),t) = 2*x(t)-7*y(t), diff(y(t),t) = 3*x(t)-8*y(t)]; 
dsolve(ode);
 

\begin{align*} x \left (t \right ) &= c_1 \,{\mathrm e}^{-t}+c_2 \,{\mathrm e}^{-5 t} \\ y \left (t \right ) &= \frac {3 c_1 \,{\mathrm e}^{-t}}{7}+c_2 \,{\mathrm e}^{-5 t} \\ \end{align*}

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 74

ode={D[x[t],t]==2*x[t]-7*y[t],D[y[t],t]==3*x[t]-8*y[t]}; 
ic={}; 
DSolve[{ode,ic},{x[t],y[t]},t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to \frac {1}{4} e^{-5 t} \left (c_1 \left (7 e^{4 t}-3\right )-7 c_2 \left (e^{4 t}-1\right )\right )\\ y(t)&\to \frac {1}{4} e^{-5 t} \left (3 c_1 \left (e^{4 t}-1\right )+c_2 \left (7-3 e^{4 t}\right )\right ) \end{align*}

✓ Sympy. Time used: 0.052 (sec). Leaf size: 31

from sympy import * 
t = symbols("t") 
x = Function("x") 
y = Function("y") 
ode=[Eq(-2*x(t) + 7*y(t) + Derivative(x(t), t),0),Eq(-3*x(t) + 8*y(t) + Derivative(y(t), t),0)] 
ics = {} 
dsolve(ode,func=[x(t),y(t)],ics=ics)
 

\[ \left [ x{\left (t \right )} = C_{1} e^{- 5 t} + \frac {7 C_{2} e^{- t}}{3}, \ y{\left (t \right )} = C_{1} e^{- 5 t} + C_{2} e^{- t}\right ] \]