74.22.2 problem 2

Internal problem ID [16578]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 6. Systems of Differential Equations. Exercises 6.1, page 282
Problem number : 2
Date solved : Monday, March 31, 2025 at 02:59:31 PM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=x \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=1 \end{align*}

✓ Maple. Time used: 0.104 (sec). Leaf size: 14

ode:=[diff(x(t),t) = x(t), diff(y(t),t) = 1]; 
dsolve(ode);
 

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

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 30

ode={D[x[t],t]==x[t],D[y[t],t]==1}; 
ic={}; 
DSolve[{ode,ic},{x[t],y[t]},t,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.064 (sec). Leaf size: 12

from sympy import * 
t = symbols("t") 
x = Function("x") 
y = Function("y") 
ode=[Eq(-x(t) + Derivative(x(t), t),0),Eq(Derivative(y(t), t) - 1,0)] 
ics = {} 
dsolve(ode,func=[x(t),y(t)],ics=ics)
 

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