70.1.13 problem 2.2 (vii)

Internal problem ID [14224]
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 : 2.2 (vii)
Date solved : Wednesday, March 05, 2025 at 10:40:25 PM
CAS classification : system_of_ODEs

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

✓ Maple. Time used: 0.032 (sec). Leaf size: 13

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

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

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 17

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

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

✓ Sympy. Time used: 0.048 (sec). Leaf size: 10

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

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