62.38.4 problem Ex 4

Internal problem ID [12944]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter IX, Miscellaneous methods for solving equations of higher order than first. Article 62. Summary. Page 144
Problem number : Ex 4
Date solved : Monday, March 31, 2025 at 07:27:42 AM
CAS classification : [[_3rd_order, _fully, _exact, _linear]]

\begin{align*} \left (x^{3}+1\right ) y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+18 x y^{\prime }+6 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 30

ode:=(x^3+1)*diff(diff(diff(y(x),x),x),x)+9*x^2*diff(diff(y(x),x),x)+18*x*diff(y(x),x)+6*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_1 \,x^{2}+c_2 x +c_3}{\left (x +1\right ) \left (x^{2}-x +1\right )} \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 31

ode=(1+x^3)*D[y[x],{x,3}]+9*x^2*D[y[x],{x,2}]+18*x*D[y[x],x]+6*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {c_3 x^2+2 c_2 x+2 c_1}{2 x^3+2} \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(9*x**2*Derivative(y(x), (x, 2)) + 18*x*Derivative(y(x), x) + (x**3 + 1)*Derivative(y(x), (x, 3)) + 6*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (x**2*(-x*Derivative(y(x), (x, 3)) - 9*Derivative(y(x), (x, 2))) - 6*y(x) - Derivative(y(x), (x, 3)))/(18*x) cannot be solved by the factorable group method