60.5.15 problem 1552

Internal problem ID [11512]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 4, linear fourth order
Problem number : 1552
Date solved : Thursday, March 13, 2025 at 08:53:32 PM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime \prime \prime }+2 x y^{\prime \prime \prime }+a y-b \,x^{2}&=0 \end{align*}

✓ Maple. Time used: 0.039 (sec). Leaf size: 94

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

\[ y = \frac {c_4 \sqrt {x}\, \operatorname {BesselY}\left (1, 2 \sqrt {-\sqrt {-a}}\, \sqrt {x}\right ) a +c_{1} \sqrt {x}\, \operatorname {BesselJ}\left (1, 2 \left (-a \right )^{{1}/{4}} \sqrt {x}\right ) a +c_{2} \sqrt {x}\, \operatorname {BesselY}\left (1, 2 \left (-a \right )^{{1}/{4}} \sqrt {x}\right ) a +c_3 \sqrt {x}\, \operatorname {BesselJ}\left (1, 2 \sqrt {-\sqrt {-a}}\, \sqrt {x}\right ) a +b \,x^{2}}{a} \]

✗ Mathematica

ode=x^2*D[y[x],{x,4}]+2*x*D[y[x],{x,3}]+a*y[x]-b*x^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Timed out

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
b = symbols("b") 
y = Function("y") 
ode = Eq(a*y(x) - b*x**2 + x**2*Derivative(y(x), (x, 4)) + 2*x*Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : solve: Cannot solve a*y(x) - b*x**2 + x**2*Derivative(y(x), (x, 4)) + 2*x*Derivative(y(x), (x, 3))