23.3.574 problem 582

Internal problem ID [6288]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 3. THE DIFFERENTIAL EQUATION IS LINEAR AND OF SECOND ORDER, page 311
Problem number : 582
Date solved : Tuesday, September 30, 2025 at 02:44:58 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} -y+x y^{\prime }+x^{5} y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 27

ode:=-y(x)+x*diff(y(x),x)+x^5*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = x \left (-3 c_2 \Gamma \left (\frac {2}{3}\right ) \Gamma \left (\frac {1}{3}, -\frac {1}{3 x^{3}}\right )+2 \pi c_2 \sqrt {3}+c_1 \right ) \]

✓ Mathematica. Time used: 0.054 (sec). Leaf size: 38

ode=-y[x] + x*D[y[x],x] + x^5*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {c_2 \Gamma \left (\frac {1}{3},-\frac {1}{3 x^3}\right )}{3^{2/3} \sqrt [3]{-\frac {1}{x^3}}}+c_1 x \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**5*Derivative(y(x), (x, 2)) + x*Derivative(y(x), x) - y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (-x**5*Derivative(y(x), (x, 2)) + y(x))/x