47.2.8 problem 15

Internal problem ID [9747]
Book : Elementary differential equations. By Earl D. Rainville, Phillip E. Bedient. Macmilliam Publishing Co. NY. 6th edition. 1981.
Section : CHAPTER 16. Nonlinear equations. Section 97. The p-discriminant equation. EXERCISES Page 314
Problem number : 15
Date solved : Tuesday, September 30, 2025 at 06:32:40 PM
CAS classification : [_dAlembert]

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

✓ Maple. Time used: 0.037 (sec). Leaf size: 982

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

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

✓ Mathematica. Time used: 58.274 (sec). Leaf size: 1489

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

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

✗ Sympy

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

Timed Out