2.2.54 Problem 50

Maple
Mathematica
Sympy

Internal problem ID [8858]
Book : Own collection of miscellaneous problems
Section : section 2.0
Problem number : 50
Date solved : Sunday, March 30, 2025 at 01:44:45 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

Does not support this form of ODE for higher order. Terminating.

Maple. Time used: 0.007 (sec). Leaf size: 51
ode:=diff(diff(diff(y(x),x),x),x)-x^3*diff(y(x),x)-x^2*y(x)-x^3 = 0; 
dsolve(ode,y(x), singsol=all);
 
y=x2+c1hypergeom([15],[35,45],x525)+c2xhypergeom([25],[45,65],x525)+c3x2hypergeom([35],[65,75],x525)

Maple trace

Methods for third order ODEs: 
--- Trying classification methods --- 
trying a quadrature 
trying high order exact linear fully integrable 
trying differential order: 3; linear nonhomogeneous with symmetry [0,1] 
trying high order linear exact nonhomogeneous 
trying differential order: 3; missing the dependent variable 
checking if the LODE is of Euler type 
trying Louvillian solutions for 3rd order ODEs, imprimitive case 
-> pFq: Equivalence to the 3F2 or one of its 3 confluent cases under a power @\ 
 Moebius 
<- pFq successful: received ODE is equivalent to the  1F2  ODE, case  c = 0
 

Maple step by step

Let’s solveddxd2dx2y(x)x3(ddxy(x))x2y(x)x3=0Highest derivative means the order of the ODE is3ddxd2dx2y(x)
Mathematica. Time used: 10.995 (sec). Leaf size: 2548
ode=D[y[x],{x,3}]-x^3*D[y[x],x]-x^2*y[x]-x^3==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Too large to display

Sympy
from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**3*Derivative(y(x), x) - x**3 - x**2*y(x) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 
NotImplementedError : The given ODE Derivative(y(x), x) + 1 + y(x)/x - Derivative(y(x), (x, 3))/x**3 cannot be solved by the factorable group method