60.7.182 problem 1802 (book 6.211)

Internal problem ID [11732]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1802 (book 6.211)
Date solved : Wednesday, March 05, 2025 at 02:42:55 PM
CAS classification : [NONE]

\begin{align*} 2 y^{3} y^{\prime \prime }+y^{4}-a^{2} x y^{2}-1&=0 \end{align*}

✗ Maple

ode:=2*y(x)^3*diff(diff(y(x),x),x)+y(x)^4-a^2*x*y(x)^2-1 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=-1 - a^2*x*y[x]^2 + y[x]^4 + 2*y[x]^3*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
y = Function("y") 
ode = Eq(-a**2*x*y(x)**2 + y(x)**4 + 2*y(x)**3*Derivative(y(x), (x, 2)) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : solve: Cannot solve -a**2*x*y(x)**2 + y(x)**4 + 2*y(x)**3*Derivative(y(x), (x, 2)) - 1