57.22.5 problem 4(e)

Internal problem ID [14516]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 4, Linear Systems. Exercises page 237
Problem number : 4(e)
Date solved : Thursday, October 02, 2025 at 09:38:04 AM
CAS classification : system_of_ODEs

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

✓ Maple. Time used: 0.105 (sec). Leaf size: 19

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

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

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 65

ode={D[x[t],t]==2*x[t]+0*y[t],D[y[t],t]==0*x[t]+2*y[t]}; 
ic={}; 
DSolve[{ode,ic},{x[t],y[t]},t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to c_1 e^{2 t}\\ y(t)&\to c_2 e^{2 t}\\ x(t)&\to c_1 e^{2 t}\\ y(t)&\to 0\\ x(t)&\to 0\\ y(t)&\to c_2 e^{2 t}\\ x(t)&\to 0\\ y(t)&\to 0 \end{align*}

✓ Sympy. Time used: 0.033 (sec). Leaf size: 17

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

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