68.5.23 problem 23

Internal problem ID [17274]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.3, page 49
Problem number : 23
Date solved : Thursday, October 02, 2025 at 02:00:37 PM
CAS classification : [_separable]

\begin{align*} x^{\prime }&=\frac {3 x t^{2}}{-t^{3}+1} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 13

ode:=diff(x(t),t) = 3*x(t)*t^2/(-t^3+1); 
dsolve(ode,x(t), singsol=all);
 

\[ x = \frac {c_1}{t^{3}-1} \]

✓ Mathematica. Time used: 0.021 (sec). Leaf size: 20

ode=D[x[t],t]==3*x[t]*t^2/(1-t^3); 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to \frac {c_1}{t^3-1}\\ x(t)&\to 0 \end{align*}

✓ Sympy. Time used: 0.144 (sec). Leaf size: 8

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(-3*t**2*x(t)/(1 - t**3) + Derivative(x(t), t),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = \frac {C_{1}}{t^{3} - 1} \]