77.1.60 problem 79 (page 120)

Internal problem ID [17871]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 79 (page 120)
Date solved : Thursday, March 13, 2025 at 11:06:14 AM
CAS classification : [_dAlembert]

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

✓ Maple. Time used: 0.132 (sec). Leaf size: 984

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

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

✓ Mathematica. Time used: 81.692 (sec). Leaf size: 1489

ode=y[x]==x*D[y[x],x]^2+D[y[x],x]^3; 
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