68.3.33 problem 28

Internal problem ID [17180]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.1, page 32
Problem number : 28
Date solved : Thursday, October 02, 2025 at 01:49:33 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=-y^{3} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&={\frac {1}{2}} \\ \end{align*}

✓ Maple. Time used: 0.063 (sec). Leaf size: 11

ode:=diff(y(t),t) = -y(t)^3; 
ic:=[y(0) = 1/2]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = \frac {1}{\sqrt {2 t +4}} \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 18

ode=D[y[t],t]==-y[t]^3; 
ic={y[0]==1/2}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {i}{\sqrt {-2 t-4}} \end{align*}

✓ Sympy. Time used: 0.250 (sec). Leaf size: 20

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

\[ y{\left (t \right )} = \frac {\sqrt {2} \sqrt {- \frac {1}{- t - 2}}}{2} \]