71.1.93 problem 120 (page 179)

Internal problem ID [19269]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 120 (page 179)
Date solved : Thursday, October 02, 2025 at 04:03:56 PM
CAS classification : [NONE]

\begin{align*} x \left (x^{2} y^{\prime }+2 y x \right ) y^{\prime \prime }+4 {y^{\prime }}^{2} x +8 x y y^{\prime }+4 y^{2}-1&=0 \end{align*}

✗ Maple

ode:=x*(x^2*diff(y(x),x)+2*x*y(x))*diff(diff(y(x),x),x)+4*x*diff(y(x),x)^2+8*x*y(x)*diff(y(x),x)+4*y(x)^2-1 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=x*(x^2*D[y[x],x]+2*x*y[x])*D[y[x],{x,2}]+4*x* D[y[x],x]^2 + 8*x*y[x]*D[y[x],x]+ 4*y[x]^2-1==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*(x**2*Derivative(y(x), x) + 2*x*y(x))*Derivative(y(x), (x, 2)) + 8*x*y(x)*Derivative(y(x), x) + 4*x*Derivative(y(x), x)**2 + 4*y(x)**2 - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (-x**3*Derivative(y(x), (x, 2)) - 8*x*y(x) + sqrt(x*(x**5*Derivative(y(x), (x, 2))**2 + 16*x**3*y(x)*Derivative(y(x), (x, 2)) - 32*x**2*y(x)*Derivative(y(x), (x, 2)) + 64*x*y(x)**2 - 64*y(x)**2 + 16)))/(8*x) cannot be solved by the factorable group method