56.2.43 problem 42

Internal problem ID [8847]
Book : Own collection of miscellaneous problems
Section : section 2.0
Problem number : 42
Date solved : Sunday, March 30, 2025 at 01:42:34 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-x^{3} y^{\prime }-x^{3} y-x^{3}&=0 \end{align*}

✗ Maple

ode:=diff(diff(y(x),x),x)-x^3*diff(y(x),x)-x^3*y(x)-x^3 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

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

NotImplementedError : The given ODE y(x) + Derivative(y(x), x) + 1 - Derivative(y(x), (x, 2))/x**3 cannot be solved by the factorable group method