72.9.2 problem 2

Internal problem ID [14719]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 3. Linear Systems. Exercises section 3.1. page 258
Problem number : 2
Date solved : Thursday, March 13, 2025 at 04:16:25 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=2 x \left (t \right )-y \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=0 \end{align*}

✓ Maple. Time used: 0.099 (sec). Leaf size: 18

ode:=[diff(x(t),t) = 2*x(t)-y(t), diff(y(t),t) = 0]; 
dsolve(ode);
 

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

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 32

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

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

✓ Sympy. Time used: 0.055 (sec). Leaf size: 15

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

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