23.4.120 problem 120

Internal problem ID [6422]
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 : 120
Date solved : Tuesday, September 30, 2025 at 02:56:31 PM
CAS classification : [NONE]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

ode=f[x]*D[f[x],x]*D[y[x],x] + f[x]^2*D[y[x],{x,2}] == g[y[x], f[x]*D[y[x],x]]; 
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)**2*Derivative(y(x), (x, 2)) + f(x)*Derivative(f(x), x)*Derivative(y(x), x) - g(y(x), f(x)*Derivative(y(x), x)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : multiple generators [_X0, g(y(x), _X0*f(x))] 
No algorithms are implemented to