23.4.176 problem 176

Internal problem ID [6478]
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 : 176
Date solved : Tuesday, September 30, 2025 at 03:01:46 PM
CAS classification : [NONE]

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

✗ Maple

ode:=2*y(x)*diff(diff(y(x),x),x) = 4*y(x)^2*(x+2*y(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}] == 4*y[x]^2*(x + 2*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(-4*(x + 2*y(x))*y(x)**2 + 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(2)*sqrt(-(2*x*y(x) + 4*y(x)**2 - Derivative(y(x), (x, 2)))*