60.7.145 problem 1762 (book 6.171)

Internal problem ID [11695]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1762 (book 6.171)
Date solved : Sunday, March 30, 2025 at 08:42:52 PM
CAS classification : [[_Painleve, `3rd`]]

\begin{align*} x y y^{\prime \prime }-x {y^{\prime }}^{2}+y y^{\prime }+x \left (d +a y^{4}\right )+y \left (c +y^{2} b \right )&=0 \end{align*}

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

ode=y[x]*(c + b*y[x]^2) + x*(d + a*y[x]^4) + y[x]*D[y[x],x] - x*D[y[x],x]^2 + x*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") 
b = symbols("b") 
c = symbols("c") 
d = symbols("d") 
y = Function("y") 
ode = Eq(x*(a*y(x)**4 + d) + x*y(x)*Derivative(y(x), (x, 2)) - x*Derivative(y(x), x)**2 + (b*y(x)**2 + c)*y(x) + y(x)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (sqrt(4*a*x**2*y(x)**4 + 4*b*x*y(x)**3 + 4*c*x*y(x) + 4*d*x**2 + 4*x**2*y(x)*Derivative(y(x), (x, 2)) + y(x)**2) + y(x))/(2*x) cannot be solved by the factorable group method