81.1.25 problem 2-23

Internal problem ID [21470]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 2. Separable differential equations
Problem number : 2-23
Date solved : Thursday, October 02, 2025 at 07:39:11 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=x^{2} y^{3} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 33

ode:=diff(y(x),x) = x^2*y(x)^3; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= -\frac {3}{\sqrt {-6 x^{3}+9 c_1}} \\ y &= \frac {3}{\sqrt {-6 x^{3}+9 c_1}} \\ \end{align*}

✓ Mathematica. Time used: 0.101 (sec). Leaf size: 59

ode=D[y[x],x]==x^2*y[x]^3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {\sqrt {\frac {3}{2}}}{\sqrt {-x^3-3 c_1}}\\ y(x)&\to \frac {\sqrt {\frac {3}{2}}}{\sqrt {-x^3-3 c_1}}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.209 (sec). Leaf size: 42

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

\[ \left [ y{\left (x \right )} = - \frac {\sqrt {6} \sqrt {- \frac {1}{C_{1} + x^{3}}}}{2}, \ y{\left (x \right )} = \frac {\sqrt {6} \sqrt {- \frac {1}{C_{1} + x^{3}}}}{2}\right ] \]