77.1.104 problem Example 2 (page 195)

Internal problem ID [17915]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : Example 2 (page 195)
Date solved : Thursday, March 13, 2025 at 11:10:29 AM
CAS classification : [[_3rd_order, _fully, _exact, _linear]]

\begin{align*} y^{\prime \prime \prime }-\frac {3 y^{\prime \prime }}{x}+\frac {6 y^{\prime }}{x^{2}}-\frac {6 y}{x^{3}}&=0 \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 16

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

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

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 19

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

\[ y(x)\to x (x (c_3 x+c_2)+c_1) \]

✓ Sympy. Time used: 0.203 (sec). Leaf size: 14

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

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