60.6.6 problem 1583

Internal problem ID [11543]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 5, linear fifth and higher order
Problem number : 1583
Date solved : Sunday, March 30, 2025 at 08:24:35 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (5\right )}+a y^{\prime \prime \prime \prime }-f&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 40

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

\[ y = \frac {f \,x^{4}}{24 a}+\frac {c_2 \,x^{3}}{6}+\frac {c_3 \,x^{2}}{2}+\frac {c_1 \,{\mathrm e}^{-a x}}{a^{4}}+c_4 x +c_5 \]

✓ Mathematica. Time used: 0.137 (sec). Leaf size: 45

ode=D[y[x],{x,5}]+a*D[y[x],{x,4}]-f==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {c_1 e^{-a x}}{a^4}+\frac {f x^4}{24 a}+x (x (c_5 x+c_4)+c_3)+c_2 \]

✓ Sympy. Time used: 0.109 (sec). Leaf size: 32

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

\[ y{\left (x \right )} = C_{1} + C_{2} x + C_{3} x^{2} + C_{4} x^{3} + C_{5} e^{- a x} + \frac {f x^{4}}{24 a} \]