54.7.21 problem 1611 (6.21)

Internal problem ID [12870]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1611 (6.21)
Date solved : Wednesday, October 01, 2025 at 02:23:46 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-3 y^{\prime }-y^{2}-2 y&=0 \end{align*}

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

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