81.1.10 problem 9

Internal problem ID [18526]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter I. Introduction. Exercises at page 13
Problem number : 9
Date solved : Thursday, March 13, 2025 at 12:11:47 PM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }+\frac {3 y^{\prime \prime }}{x}&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 14

ode:=diff(diff(diff(y(x),x),x),x)+3/x*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y \left (x \right ) = c_{1} +\frac {c_{2}}{x}+c_3 x \]

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 21

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

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

✓ Sympy. Time used: 0.069 (sec). Leaf size: 10

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

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