89.29.9 problem 15

Internal problem ID [24916]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 16. Equations of order one and higher degree. Exercises at page 235
Problem number : 15
Date solved : Thursday, October 02, 2025 at 10:49:29 PM
CAS classification : [_dAlembert]

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

✓ Maple. Time used: 0.015 (sec). Leaf size: 993

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: 54.176 (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