54.5.40 problem 1577

Internal problem ID [12836]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 4, linear fourth order
Problem number : 1577
Date solved : Wednesday, October 01, 2025 at 02:22:23 AM
CAS classification : [[_high_order, _quadrature]]

\begin{align*} f y^{\prime \prime \prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 21

ode:=f*diff(diff(diff(diff(y(x),x),x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {1}{6} c_1 \,x^{3}+\frac {1}{2} c_2 \,x^{2}+c_3 x +c_4 \]

✓ Mathematica. Time used: 8.71 (sec). Leaf size: 41

ode=Derivative[2][f][x]*D[y[x],{x,2}] + 2*Derivative[1][f][x]*Derivative[3][y][x] + f[x]*Derivative[4][y][x] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \int _1^x\int _1^{K[2]}\frac {c_1+c_2 K[1]}{f(K[1])}dK[1]dK[2]+c_4 x+c_3 \end{align*}

✓ Sympy. Time used: 0.031 (sec). Leaf size: 17

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

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