60.6.9 problem 1586

Internal problem ID [11546]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 5, linear fifth and higher order
Problem number : 1586
Date solved : Sunday, March 30, 2025 at 08:24:38 PM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} x y^{\left (5\right )}-\left (a A_{1} -A_{0} \right ) x -A_{1} -\left (\left (a A_{2} -A_{1} \right ) x +A_{2} \right ) y^{\prime }&=0 \end{align*}

✗ Maple

ode:=x*diff(diff(diff(diff(diff(y(x),x),x),x),x),x)-(A__1*a-A__0)*x-A__1-((A__2*a-A__1)*x+A__2)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=x*D[y[x],{x,5}]-((a*A1-A0)*x+A1)-((a*A2-A1)*x+A2)*D[y[x],x]== 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
A__0 = symbols("A__0") 
A__1 = symbols("A__1") 
A__2 = symbols("A__2") 
a = symbols("a") 
y = Function("y") 
ode = Eq(-A__1 - x*(-A__0 + A__1*a) + x*Derivative(y(x), (x, 5)) - (A__2 + x*(-A__1 + A__2*a))*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (A__0*x - A__1*a*x - A__1 + x*Derivative(y(x), (x, 5)))/(-A__1*x + A__2*a*x + A__2) cannot be solved by the factorable group method