60.5.30 problem 1567

Internal problem ID [11527]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 4, linear fourth order
Problem number : 1567
Date solved : Wednesday, March 05, 2025 at 02:27:22 PM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} x^{4} y^{\prime \prime \prime \prime }+8 x^{3} y^{\prime \prime \prime }+12 x^{2} y^{\prime \prime }&=0 \end{align*}

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

ode:=x^4*diff(diff(diff(diff(y(x),x),x),x),x)+8*x^3*diff(diff(diff(y(x),x),x),x)+12*x^2*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_{1} +\frac {c_{2}}{x}+\frac {c_3}{x^{2}}+c_4 x \]

✓ Mathematica. Time used: 0.023 (sec). Leaf size: 27

ode=12*x^2*D[y[x],{x,2}] + 8*x^3*Derivative[3][y][x] + x^4*Derivative[4][y][x] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {3 c_2 x+c_1}{6 x^2}+c_4 x+c_3 \]

✓ Sympy. Time used: 0.110 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**4*Derivative(y(x), (x, 4)) + 8*x**3*Derivative(y(x), (x, 3)) + 12*x**2*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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