15.20.5 problem 5

Internal problem ID [3313]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 38, page 173
Problem number : 5
Date solved : Sunday, March 30, 2025 at 01:34:40 AM
CAS classification : [_dAlembert]

\begin{align*} x {y^{\prime }}^{3}&=y y^{\prime }+1 \end{align*}

✓ Maple. Time used: 0.064 (sec). Leaf size: 1805

ode:=x*diff(y(x),x)^3 = y(x)*diff(y(x),x)+1; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Mathematica. Time used: 142.19 (sec). Leaf size: 21579

ode=x*D[y[x],x]^3==y[x]*D[y[x],x]+1; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Too large to display

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*Derivative(y(x), x)**3 - y(x)*Derivative(y(x), x) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out