70.1.5 problem 2.1 (v)

Internal problem ID [14216]
Book : Nonlinear Ordinary Differential Equations by D.W.Jordna and P.Smith. 4th edition 1999. Oxford Univ. Press. NY
Section : Chapter 2. Plane autonomous systems and linearization. Problems page 79
Problem number : 2.1 (v)
Date solved : Wednesday, March 05, 2025 at 10:40:17 PM
CAS classification : system_of_ODEs

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

✓ Maple. Time used: 0.042 (sec). Leaf size: 30

ode:=[diff(x(t),t) = 4*x(t)-2*y(t), diff(y(t),t) = 3*x(t)-y(t)]; 
dsolve(ode);
 

\begin{align*} x \left (t \right ) &= c_{1} {\mathrm e}^{2 t}+c_{2} {\mathrm e}^{t} \\ y \left (t \right ) &= c_{1} {\mathrm e}^{2 t}+\frac {3 c_{2} {\mathrm e}^{t}}{2} \\ \end{align*}

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 56

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

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

✓ Sympy. Time used: 0.088 (sec). Leaf size: 31

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

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