54.7.88 problem 1699 (book 6.108)

Internal problem ID [12937]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1699 (book 6.108)
Date solved : Wednesday, October 01, 2025 at 02:46:29 AM
CAS classification : [NONE]

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

✗ Maple

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

\[ \text {No solution found} \]

✓ Mathematica. Time used: 0.495 (sec). Leaf size: 63

ode=-b - a*x + D[y[x],x]^2 + y[x]*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\sqrt {\frac {a x^3}{3}+b x^2+c_2 x+2 c_1}\\ y(x)&\to \sqrt {\frac {a x^3}{3}+b x^2+c_2 x+2 c_1} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
b = symbols("b") 
y = Function("y") 
ode = Eq(-a*x - b + y(x)**2 + y(x)*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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