83.10.9 problem 9

Internal problem ID [21978]
Book : Differential Equations By Kaj L. Nielsen. Second edition 1966. Barnes and nobel. 66-28306
Section : Chapter IV. First order differential equations of higher degree. Ex. XI at page 69
Problem number : 9
Date solved : Thursday, October 02, 2025 at 08:21:17 PM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} 2 x +y y^{\prime } \left (4 {y^{\prime }}^{2}+6\right )&=0 \end{align*}

✓ Maple. Time used: 0.045 (sec). Leaf size: 776

ode:=2*x+y(x)*diff(y(x),x)*(4*diff(y(x),x)^2+6) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✗ Mathematica

ode=2*x+y[x]*D[y[x],x]*(4*D[y[x],x]^2+6)==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Timed out

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x + (4*Derivative(y(x), x)**2 + 6)*y(x)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out