67.9.34 problem 14.5 (d)

Internal problem ID [16582]
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 : 14.5 (d)
Date solved : Thursday, October 02, 2025 at 01:36:36 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} x^{3} y^{\prime \prime \prime }-4 y^{\prime \prime }+10 y^{\prime }-12 y&=0 \end{align*}

✗ Maple

ode:=x^3*diff(diff(diff(y(x),x),x),x)-4*diff(diff(y(x),x),x)+10*diff(y(x),x)-12*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=x^3*D[y[x],{x,3}]-4*D[y[x],{x,2}]+10*D[y[x],x]-12*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**3*Derivative(y(x), (x, 3)) - 12*y(x) + 10*Derivative(y(x), x) - 4*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE x**3*Derivative(y(x), (x, 3))/10 - 6*y(x)/5 + Derivative(y(x), x) - 2*Derivative(y(x), (x, 2))/5 cannot be solved by the factorable group method