23.4.139 problem 139

Internal problem ID [6441]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 4. THE NONLINEAR EQUATION OF SECOND ORDER, page 380
Problem number : 139
Date solved : Tuesday, September 30, 2025 at 02:56:54 PM
CAS classification : [NONE]

\begin{align*} y y^{\prime \prime }&=y^{2} \left (f \left (x \right ) y+g^{\prime }\left (x \right )\right )+y^{\prime }+{y^{\prime }}^{2} \end{align*}

✗ Maple

ode:=y(x)*diff(diff(y(x),x),x) = y(x)^2*(f(x)*y(x)+diff(g(x),x))+diff(y(x),x)+diff(y(x),x)^2; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=y[x]*D[y[x],{x,2}] == y[x]^2*(f[x]*y[x] + D[g[x],x]) + D[y[x],x] + D[y[x],x]^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

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

NotImplementedError : The given ODE -sqrt(-4*f(x)*y(x)**3 - 4*y(x)**2*Derivative(g(x), x) + 4*y(x)*D