60.7.40 problem 1637 (6.47)

Internal problem ID [11590]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1637 (6.47)
Date solved : Sunday, March 30, 2025 at 08:30:05 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

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