60.7.183 problem 1803 (book 6.212)

Internal problem ID [11733]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1803 (book 6.212)
Date solved : Wednesday, March 05, 2025 at 02:42:56 PM
CAS classification : [NONE]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

ode=-c - b*x - a*x^2 + y[x]^2*D[y[x],x]^2 + 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") 
b = symbols("b") 
c = symbols("c") 
y = Function("y") 
ode = Eq(-a*x**2 - b*x - c + 2*y(x)**3*Derivative(y(x), (x, 2)) + y(x)**2*Derivative(y(x), x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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