67.9.10 problem 14.1 (j)

Internal problem ID [16558]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 14. Higher order equations and the reduction of order method. Additional exercises page 277
Problem number : 14.1 (j)
Date solved : Thursday, October 02, 2025 at 01:36:28 PM
CAS classification : [[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]]

\begin{align*} y y^{\prime \prime \prime }+6 y^{\prime \prime }+3 y^{\prime }&=y \end{align*}

✗ Maple

ode:=y(x)*diff(diff(diff(y(x),x),x),x)+6*diff(diff(y(x),x),x)+3*diff(y(x),x) = y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=y[x]*D[y[x],{x,3}]+6*D[y[x],{x,2}]+3*D[y[x],x]==y[x]; 
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, 3)) - y(x) + 3*Derivative(y(x), x) + 6*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE y(x)*Derivative(y(x), (x, 3))/3 - y(x)/3 + Derivative(y(x), x) + 2*Derivative(y(x), (x, 2)) cannot be solved by the factorable group method