50.1.45 problem 45

Internal problem ID [10043]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 45
Date solved : Tuesday, September 30, 2025 at 06:50:57 PM
CAS classification : [_dAlembert]

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

✓ Maple. Time used: 0.072 (sec). Leaf size: 1791

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

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

✓ Mathematica. Time used: 111.463 (sec). Leaf size: 20717

ode=D[y[x],x]*y[x]==1-x*(D[y[x],x])^3; 
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