82.12.19 problem Ex. 21

Internal problem ID [18713]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter II. Equations of the first order and of the first degree. Examples on chapter II at page 29
Problem number : Ex. 21
Date solved : Monday, March 31, 2025 at 06:02:23 PM
CAS classification : [_Bernoulli]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 35

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

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

✓ Mathematica. Time used: 7.292 (sec). Leaf size: 50

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

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

✓ Sympy. Time used: 0.801 (sec). Leaf size: 39

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

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