23.5.151 problem 151

Internal problem ID [6760]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 5. THE EQUATION IS LINEAR AND OF ORDER GREATER THAN TWO, page 410
Problem number : 151
Date solved : Tuesday, September 30, 2025 at 03:51:27 PM
CAS classification : [[_high_order, _missing_x], [_high_order, _with_linear_symmetries]]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

NotImplementedError : solve: Cannot solve y(x)**2 - 2*Derivative(y(x), (x, 3)) + Derivative(y(x), (x