23.4.250 problem 250

Internal problem ID [6552]
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 : 250
Date solved : Tuesday, September 30, 2025 at 03:04:21 PM
CAS classification : [NONE]

\begin{align*} 2 \left (1-y\right ) y y^{\prime \prime }&=4 y \left (f \left (x \right )+g \left (x \right ) y\right ) y^{\prime }+\left (1-3 y\right ) {y^{\prime }}^{2} \end{align*}

✗ Maple

ode:=2*(1-y(x))*y(x)*diff(diff(y(x),x),x) = 4*y(x)*(f(x)+g(x)*y(x))*diff(y(x),x)+(1-3*y(x))*diff(y(x),x)^2; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=2*(1 - y[x])*y[x]*D[y[x],{x,2}] == 4*y[x]*(f[x] + g[x]*y[x])*D[y[x],x] + (1 - 3*y[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(-(1 - 3*y(x))*Derivative(y(x), x)**2 + (2 - 2*y(x))*y(x)*Derivative(y(x), (x, 2)) - 4*(f(x) + g(x)*y(x))*y(x)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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