62.15.1 problem Ex 1

Internal problem ID [12817]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter IV, differential equations of the first order and higher degree than the first. Article 26. Equations solvable for \(x\). Page 55
Problem number : Ex 1
Date solved : Monday, March 31, 2025 at 07:11:20 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} x +y^{\prime } y \left (2 {y^{\prime }}^{2}+3\right )&=0 \end{align*}

✓ Maple. Time used: 0.106 (sec). Leaf size: 768

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

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

✗ Mathematica

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

Timed out

✗ Sympy

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

Timed Out