87.30.11 problem 11

Internal problem ID [23910]
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 8. Nonlinear differential equations and systems. Exercise at page 310
Problem number : 11
Date solved : Thursday, October 02, 2025 at 09:46:28 PM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=4 x \left (t \right )-6 y \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=8 x \left (t \right )-10 y \left (t \right ) \end{align*}

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

ode:=[diff(x(t),t) = 4*x(t)-6*y(t), diff(y(t),t) = 8*x(t)-10*y(t)]; 
dsolve(ode);
 

\begin{align*} x \left (t \right ) &= c_1 \,{\mathrm e}^{-4 t}+c_2 \,{\mathrm e}^{-2 t} \\ y \left (t \right ) &= \frac {4 c_1 \,{\mathrm e}^{-4 t}}{3}+c_2 \,{\mathrm e}^{-2 t} \\ \end{align*}

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 68

ode={D[x[t],t]==4*x[t]-6*y[t],D[y[t],t]==8*x[t]-10*y[t]}; 
ic={}; 
DSolve[{ode,ic},{x[t],y[t]},t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to e^{-4 t} \left (c_1 \left (4 e^{2 t}-3\right )-3 c_2 \left (e^{2 t}-1\right )\right )\\ y(t)&\to e^{-4 t} \left (4 c_1 \left (e^{2 t}-1\right )+c_2 \left (4-3 e^{2 t}\right )\right ) \end{align*}

✓ Sympy. Time used: 0.056 (sec). Leaf size: 34

from sympy import * 
t = symbols("t") 
x = Function("x") 
y = Function("y") 
ode=[Eq(-4*x(t) + 6*y(t) + Derivative(x(t), t),0),Eq(-8*x(t) + 10*y(t) + Derivative(y(t), t),0)] 
ics = {} 
dsolve(ode,func=[x(t),y(t)],ics=ics)
 

\[ \left [ x{\left (t \right )} = \frac {3 C_{1} e^{- 4 t}}{4} + C_{2} e^{- 2 t}, \ y{\left (t \right )} = C_{1} e^{- 4 t} + C_{2} e^{- 2 t}\right ] \]