68.22.4 problem 4

Internal problem ID [17938]
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 : 4
Date solved : Sunday, October 12, 2025 at 05:33:14 AM
CAS classification : system_of_ODEs

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

✓ Maple. Time used: 0.123 (sec). Leaf size: 20

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

\begin{align*} \left \{x \left (t \right ) &= \frac {1}{-t +c_2}\right \} \\ \{y \left (t \right ) &= {\mathrm e}^{t}+c_1\} \\ \end{align*}

✓ Mathematica. Time used: 0.073 (sec). Leaf size: 36

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

\begin{align*} x(t)&\to -\frac {1}{t+c_1}\\ y(t)&\to e^t+c_2\\ x(t)&\to 0\\ y(t)&\to e^t+c_2 \end{align*}

✗ Sympy

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

NotImplementedError :