23.4.182 problem 182

Internal problem ID [6484]
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 : 182
Date solved : Tuesday, September 30, 2025 at 03:01:50 PM
CAS classification : [NONE]

\begin{align*} 2 y y^{\prime \prime }&=8 y^{3}-2 y^{2} \left (f \left (x \right )^{2}+f^{\prime }\left (x \right )\right )-3 f \left (x \right ) y y^{\prime }+{y^{\prime }}^{2} \end{align*}

✗ Maple

ode:=2*y(x)*diff(diff(y(x),x),x) = 8*y(x)^3-2*y(x)^2*(f(x)^2+diff(f(x),x))-3*f(x)*y(x)*diff(y(x),x)+diff(y(x),x)^2; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=2*y[x]*D[y[x],{x,2}] == 8*y[x]^3 - 2*y[x]^2*(f[x]^2 + D[f[x],x]) - 3*f[x]*y[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(2*(f(x)**2 + Derivative(f(x), x))*y(x)**2 + 3*f(x)*y(x)*Derivative(y(x), x) - 8*y(x)**3 + 2*y(x)*Derivative(y(x), (x, 2)) - Derivative(y(x), x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -sqrt((17*f(x)**2*y(x) - 32*y(x)**2 + 8*y(x)*Derivative(f(x), x)