54.7.122 problem 1735 (book 6.144)

Internal problem ID [12971]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1735 (book 6.144)
Date solved : Wednesday, October 01, 2025 at 02:55:29 AM
CAS classification : [NONE]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

ode=1 + 2*x*y[x]^2 + a*y[x]^3 - D[y[x],x]^2 + 2*y[x]*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*y(x)**3 + 2*x*y(x)**2 + 2*y(x)*Derivative(y(x), (x, 2)) - Derivative(y(x), x)**2 + 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -sqrt(a*y(x)**3 + 2*x*y(x)**2 + 2*y(x)*Derivative(y(x), (x, 2)) + 1) + Derivative(y(x), x) cannot be solved by the factorable group method