85.5.2 problem 5

Internal problem ID [22448]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 1. Differential equations in general. Section 1.3. B Exercises at page 22
Problem number : 5
Date solved : Thursday, October 02, 2025 at 08:39:40 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 23

ode:=diff(y(x),x) = y(x)^3; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {1}{\sqrt {-2 x +c_1}} \\ y &= -\frac {1}{\sqrt {-2 x +c_1}} \\ \end{align*}

✓ Mathematica. Time used: 0.083 (sec). Leaf size: 51

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

\begin{align*} y(x)&\to -\frac {1}{\sqrt {2} \sqrt {-x-c_1}}\\ y(x)&\to \frac {1}{\sqrt {2} \sqrt {-x-c_1}}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.180 (sec). Leaf size: 39

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

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