59.1.485 problem 501

Internal problem ID [9657]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 501
Date solved : Sunday, March 30, 2025 at 02:39:36 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+x^{6} y^{\prime }+7 x^{5} y&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 65

ode:=diff(diff(y(x),x),x)+x^6*diff(y(x),x)+7*x^5*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {c_2 \,{\mathrm e}^{-\frac {x^{7}}{7}} x^{7} \Gamma \left (\frac {6}{7}\right )}{\left (-x^{7}\right )^{{6}/{7}}}+\frac {c_2 \,{\mathrm e}^{-\frac {x^{7}}{7}} x^{7} \Gamma \left (\frac {6}{7}, -\frac {x^{7}}{7}\right )}{\left (-x^{7}\right )^{{6}/{7}}}+c_1 \,{\mathrm e}^{-\frac {x^{7}}{7}} x +c_2 7^{{1}/{7}} \]

✓ Mathematica. Time used: 0.08 (sec). Leaf size: 53

ode=D[y[x],{x,2}]+x^6*D[y[x],x]+7*x^5*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{49} e^{-\frac {x^7}{7}} \left (49 c_1 x-7^{6/7} c_2 \sqrt [7]{-x^7} \Gamma \left (-\frac {1}{7},-\frac {x^7}{7}\right )\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**6*Derivative(y(x), x) + 7*x**5*y(x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False