54.5.12 problem 1549

Internal problem ID [12808]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 4, linear fourth order
Problem number : 1549
Date solved : Wednesday, October 01, 2025 at 02:22:12 AM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} x y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }-24&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 26

ode:=x*diff(diff(diff(diff(y(x),x),x),x),x)+5*diff(diff(diff(y(x),x),x),x)-24 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {c_1}{24 x^{2}}+\frac {4 x^{3}}{5}+\frac {c_2 \,x^{2}}{2}+c_3 x +c_4 \]

✓ Mathematica. Time used: 0.021 (sec). Leaf size: 34

ode=-24 + 5*Derivative[3][y][x] + x*Derivative[4][y][x] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {4 x^3}{5}+c_4 x^2-\frac {c_1}{24 x^2}+c_3 x+c_2 \end{align*}

✓ Sympy. Time used: 0.144 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*Derivative(y(x), (x, 4)) + 5*Derivative(y(x), (x, 3)) - 24,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + \frac {C_{2}}{x^{2}} + C_{3} x + C_{4} x^{2} + \frac {4 x^{3}}{5} \]