23.4.71 problem 71

Internal problem ID [6373]
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 : 71
Date solved : Tuesday, September 30, 2025 at 02:53:35 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✗ Maple

ode:=diff(diff(y(x),x),x) = f(x,diff(y(x),x)/y(x))*y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

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

NotImplementedError : 
No algorithms are implemented to solve equation _Dummy_37 - f(x, _X0/y(x))*y(