23.6.10 problem 10

Internal problem ID [6809]
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 : 10
Date solved : Friday, October 03, 2025 at 02:09:54 AM
CAS classification : [[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]]

\begin{align*} 15 {y^{\prime }}^{3}-18 y y^{\prime } y^{\prime \prime }+4 y^{2} y^{\prime \prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.077 (sec). Leaf size: 77

ode:=15*diff(y(x),x)^3-18*y(x)*diff(y(x),x)*diff(diff(y(x),x),x)+4*y(x)^2*diff(diff(diff(y(x),x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= 0 \\ y &= {\mathrm e}^{\int \operatorname {RootOf}\left (-2 \int _{}^{\textit {\_Z}}\frac {1}{\textit {\_h}^{2}+\sqrt {c_1 \left (\textit {\_h}^{2}+c_1 \right )}+c_1}d \textit {\_h} +x +c_2 \right )d x +c_3} \\ y &= {\mathrm e}^{\int \operatorname {RootOf}\left (2 \int _{}^{\textit {\_Z}}-\frac {1}{\textit {\_h}^{2}-\sqrt {c_1 \left (\textit {\_h}^{2}+c_1 \right )}+c_1}d \textit {\_h} +x +c_2 \right )d x +c_3} \\ \end{align*}

✓ Mathematica. Time used: 0.072 (sec). Leaf size: 19

ode=15*D[y[x],x]^3 - 18*y[x]*D[y[x],x]*D[y[x],{x,2}] + 4*y[x]^2*D[y[x],{x,3}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{(x (c_3 x+c_2)+c_1){}^2} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*y(x)**2*Derivative(y(x), (x, 3)) - 18*y(x)*Derivative(y(x), x)*Derivative(y(x), (x, 2)) + 15*Derivative(y(x), x)**3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE (sqrt(1296*y(x)**4*Derivative(y(x), (x, 3))**2/25 - 23328*y(x)**