60.5.8 problem 1541

Internal problem ID [11505]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 4, linear fourth order
Problem number : 1541
Date solved : Wednesday, March 05, 2025 at 02:27:07 PM
CAS classification : [[_high_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime \prime }+\left (a \,x^{2}+b \lambda +c \right ) y^{\prime \prime }+\left (a \,x^{2}+\beta \lambda +\gamma \right ) y&=0 \end{align*}

✗ Maple

ode:=diff(diff(diff(diff(y(x),x),x),x),x)+(a*x^2+b*lambda+c)*diff(diff(y(x),x),x)+(a*x^2+beta*lambda+gamma)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=(\[Gamma] + \[Beta]*\[Lambda] + a*x^2)*y[x] + (c + b*\[Lambda] + a*x^2)*D[y[x],{x,2}] + Derivative[4][y][x] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
BETA = symbols("BETA") 
Gamma = symbols("Gamma") 
a = symbols("a") 
b = symbols("b") 
c = symbols("c") 
cg = symbols("cg") 
y = Function("y") 
ode = Eq((BETA*cg + Gamma + a*x**2)*y(x) + (a*x**2 + b*cg + c)*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : solve: Cannot solve (BETA*cg + Gamma + a*x**2)*y(x) + (a*x**2 + b*cg + c)*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 4))