60.7.69 problem 1678 (book 6.87)

Internal problem ID [11619]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1678 (book 6.87)
Date solved : Wednesday, March 05, 2025 at 02:35:04 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

ode=b*x + a*y[x]*D[y[x],x]^2 + x^2*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") 
b = symbols("b") 
y = Function("y") 
ode = Eq(a*y(x)*Derivative(y(x), x)**2 + b*x + x**2*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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