23.5.83 problem 83

Internal problem ID [6692]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 5. THE EQUATION IS LINEAR AND OF ORDER GREATER THAN TWO, page 410
Problem number : 83
Date solved : Tuesday, September 30, 2025 at 03:50:53 PM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} 6 y^{\prime }+6 x y^{\prime \prime }+x^{2} y^{\prime \prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 16

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

\[ y = c_1 +\frac {c_2}{x}+\frac {c_3}{x^{2}} \]

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 24

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

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

✓ Sympy. Time used: 0.101 (sec). Leaf size: 12

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

\[ y{\left (x \right )} = C_{1} + \frac {C_{2}}{x^{2}} + \frac {C_{3}}{x} \]