60.4.39 problem 1495

Internal problem ID [11462]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 3, linear third order
Problem number : 1495
Date solved : Wednesday, March 05, 2025 at 02:26:22 PM
CAS classification : [[_3rd_order, _missing_y]]

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

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

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

\[ y = c_{1} +\frac {c_{2}}{x}+\frac {c_3}{x^{2}} \]

✓ Mathematica. Time used: 0.021 (sec). Leaf size: 23

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

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

✓ Sympy. Time used: 0.168 (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)
 

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