56.15.4 problem Ex 4

Internal problem ID [14172]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter IV, differential equations of the first order and higher degree than the first. Article 26. Equations solvable for \(x\). Page 55
Problem number : Ex 4
Date solved : Thursday, October 02, 2025 at 09:18:04 AM
CAS classification : [[_1st_order, _with_linear_symmetries]]

\begin{align*} {y^{\prime }}^{3}-4 x y y^{\prime }+8 y^{2}&=0 \end{align*}

✓ Maple. Time used: 0.078 (sec). Leaf size: 29

ode:=diff(y(x),x)^3-4*x*y(x)*diff(y(x),x)+8*y(x)^2 = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {4 x^{3}}{27} \\ y &= 0 \\ y &= \frac {\left (4 c_1 x -1\right )^{2}}{64 c_1^{3}} \\ \end{align*}

✗ Mathematica

ode=(D[y[x],x])^3-4*x*y[x]*D[y[x],x]+8*y[x]^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Timed out

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-4*x*y(x)*Derivative(y(x), x) + 8*y(x)**2 + Derivative(y(x), x)**3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out