72.12.12 problem 21(a)

Internal problem ID [14780]
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 3.5 page 327
Problem number : 21(a)
Date solved : Thursday, March 13, 2025 at 04:18:50 AM
CAS classification : system_of_ODEs

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

✓ Maple. Time used: 0.037 (sec). Leaf size: 14

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

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

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 18

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

\begin{align*} x(t)\to 2 c_2 t+c_1 \\ y(t)\to c_2 \\ \end{align*}

✓ Sympy. Time used: 0.046 (sec). Leaf size: 14

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

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