54.5.23 problem 1560

Internal problem ID [12819]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 4, linear fourth order
Problem number : 1560
Date solved : Wednesday, October 01, 2025 at 02:22:16 AM
CAS classification : [[_high_order, _missing_y]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 18

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

\[ y = c_1 +c_2 \ln \left (x \right )+c_3 x +\frac {c_4}{x} \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 29

ode=6*x*D[y[x],{x,2}] + 6*x^2*Derivative[3][y][x] + x^3*Derivative[4][y][x] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {c_1}{2 x}+c_4 x-c_2 \log (x)+c_2+c_3 \end{align*}

✓ Sympy. Time used: 0.064 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**3*Derivative(y(x), (x, 4)) + 6*x**2*Derivative(y(x), (x, 3)) + 6*x*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + \frac {C_{2}}{x} + C_{3} x + C_{4} \log {\left (x \right )} \]