40.6.9 problem 18

Internal problem ID [6689]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 10. Singular solutions, Extraneous loci. Supplemetary problems. Page 74
Problem number : 18
Date solved : Sunday, March 30, 2025 at 11:18:22 AM
CAS classification : [[_1st_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.251 (sec). Leaf size: 40

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

\begin{align*} y &= -\frac {2 \sqrt {3}\, x^{3}}{9} \\ y &= \frac {2 \sqrt {3}\, x^{3}}{9} \\ y &= \frac {x^{2}}{2 c_1}-\frac {1}{8 c_1^{3}} \\ \end{align*}

✗ Mathematica

ode=D[y[x],x]^3-4*x^4*D[y[x],x]+8*x^3*y[x]==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**4*Derivative(y(x), x) + 8*x**3*y(x) + Derivative(y(x), x)**3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out