23.4.26 problem 26

Internal problem ID [6328]
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 : 26
Date solved : Tuesday, September 30, 2025 at 02:47:27 PM
CAS classification : [[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

NotImplementedError : The given ODE -(-y(x)*Derivative(f(x), x) + Derivative(y(x), (x, 2)))/(f(x) -