23.4.141 problem 141

Internal problem ID [6443]
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 : 141
Date solved : Tuesday, September 30, 2025 at 02:56:55 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y-x y^{\prime }+{y^{\prime }}^{2}+y y^{\prime \prime }&=0 \end{align*}

✗ Maple

ode:=y(x)-x*diff(y(x),x)+diff(y(x),x)^2+y(x)*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=y[x] - x*D[y[x],x] + D[y[x],x]^2 + y[x]*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*Derivative(y(x), x) + y(x)*Derivative(y(x), (x, 2)) + y(x) + Derivative(y(x), x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -x/2 - sqrt(x**2 - 4*y(x)*Derivative(y(x), (x, 2)) - 4*y(x))/2 +