23.1.89 problem 83

Internal problem ID [4696]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 83
Date solved : Tuesday, September 30, 2025 at 08:15:21 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 27

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

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

✓ Mathematica. Time used: 0.099 (sec). Leaf size: 44

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

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

✓ Sympy. Time used: 0.189 (sec). Leaf size: 29

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

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