56.3.5 problem Ex 5

Internal problem ID [14092]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter 2, differential equations of the first order and the first degree. Article 10. Homogeneous equations. Page 15
Problem number : Ex 5
Date solved : Thursday, October 02, 2025 at 09:13:00 AM
CAS classification : [_separable]

\begin{align*} y^{3}+x^{3} y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 30

ode:=y(x)^3+x^3*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.328 (sec). Leaf size: 45

ode=y[x]^3+x^3*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.337 (sec). Leaf size: 36

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

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