71.8.13 problem 6 (c)

Internal problem ID [14376]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.4.4, page 115
Problem number : 6 (c)
Date solved : Monday, March 31, 2025 at 12:20:02 PM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (-1\right )&=-1 \end{align*}

✓ Maple. Time used: 0.078 (sec). Leaf size: 13

ode:=diff(y(x),x) = y(x)^3; 
ic:=y(-1) = -1; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = -\frac {1}{\sqrt {-2 x -1}} \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 16

ode=D[y[x],x]==y[x]^3; 
ic={y[-1]==-1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -\frac {1}{\sqrt {-2 x-1}} \]

✓ Sympy. Time used: 0.340 (sec). Leaf size: 22

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

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