60.5.7 problem 1540

Internal problem ID [11504]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 4, linear fourth order
Problem number : 1540
Date solved : Sunday, March 30, 2025 at 08:23:48 PM
CAS classification : [[_high_order, _with_linear_symmetries]]

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

✗ Maple

ode:=diff(diff(diff(diff(y(x),x),x),x),x)+a*(b*x-1)*diff(diff(y(x),x),x)+a*b*diff(y(x),x)+lambda*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=\[Lambda]*y[x] + a*b*D[y[x],x] + a*(-1 + b*x)*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") 
a = symbols("a") 
b = symbols("b") 
lambda_ = symbols("lambda_") 
y = Function("y") 
ode = Eq(a*b*Derivative(y(x), x) + a*(b*x - 1)*Derivative(y(x), (x, 2)) + lambda_*y(x) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (-a*b*x*Derivative(y(x), (x, 2)) + a*Derivative(y(x), (x, 2)) - lambda_*y(x) - Derivative(y(x), (x, 4)))/(a*b) cannot be solved by the factorable group method