23.6.3 problem 3

Internal problem ID [6802]
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 : 3
Date solved : Tuesday, September 30, 2025 at 03:51:50 PM
CAS classification : [[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

ode=a*y[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") 
a = symbols("a") 
y = Function("y") 
ode = Eq(a*y(x)*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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