23.6.2 problem 2

Internal problem ID [6801]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 6. THE EQUATION IS NONLINEAR AND OF ORDER GREATER THAN TWO, page 427
Problem number : 2
Date solved : Tuesday, September 30, 2025 at 03:51:50 PM
CAS classification : [[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

ode=-(y[x]*D[y[x],x]) + D[y[x],x]^2 + D[y[x],{x,3}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-y(x)*Derivative(y(x), x) + Derivative(y(x), x)**2 + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -sqrt(y(x)**2 - 4*Derivative(y(x), (x, 3)))/2 - y(x)/2 + Derivat