60.7.129 problem 1744 (book 6.153)

Internal problem ID [11679]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1744 (book 6.153)
Date solved : Sunday, March 30, 2025 at 08:41:46 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 2 y^{\prime \prime } y-6 {y^{\prime }}^{2}+\left (1+a y^{3}\right ) y^{2}&=0 \end{align*}

✓ Maple. Time used: 0.028 (sec). Leaf size: 77

ode:=2*diff(diff(y(x),x),x)*y(x)-6*diff(y(x),x)^2+(1+a*y(x)^3)*y(x)^2 = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= 0 \\ -2 \int _{}^{y}\frac {1}{\sqrt {4 c_1 \,\textit {\_a}^{4}+4 \textit {\_a}^{3} a +1}\, \textit {\_a}}d \textit {\_a} -x -c_2 &= 0 \\ 2 \int _{}^{y}\frac {1}{\sqrt {4 c_1 \,\textit {\_a}^{4}+4 \textit {\_a}^{3} a +1}\, \textit {\_a}}d \textit {\_a} -x -c_2 &= 0 \\ \end{align*}

✓ Mathematica. Time used: 37.208 (sec). Leaf size: 2761

ode=y[x]^2*(1 + a*y[x]^3) - 6*D[y[x],x]^2 + 2*y[x]*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Too large to display

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
y = Function("y") 
ode = Eq((a*y(x)**3 + 1)*y(x)**2 + 2*y(x)*Derivative(y(x), (x, 2)) - 6*Derivative(y(x), x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -sqrt(6)*sqrt((a*y(x)**4 + y(x) + 2*Derivative(y(x), (x, 2)))*y(x))/6 + Derivative(y(x), x) cannot be solved by the factorable group method