54.7.5 problem 1595 (6.5)

Internal problem ID [12854]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1595 (6.5)
Date solved : Wednesday, October 01, 2025 at 02:22:36 AM
CAS classification : [NONE]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

ode=c + b*x + a*y[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*y(x)**2 + b*x + c + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : solve: Cannot solve a*y(x)**2 + b*x + c + Derivative(y(x), (x, 2))