59.1.65 problem 67

Internal problem ID [9237]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 67
Date solved : Wednesday, March 05, 2025 at 07:38:17 AM
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: 0.006 (sec). Leaf size: 62

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);
 

\[ y = -\frac {\left (-c_{1} {\mathrm e}^{-\frac {x^{7}}{7}} x -c_{2} 7^{{1}/{7}}\right ) \left (-x^{7}\right )^{{6}/{7}}+x^{7} c_{2} {\mathrm e}^{-\frac {x^{7}}{7}} \left (\Gamma \left (\frac {6}{7}\right )-\Gamma \left (\frac {6}{7}, -\frac {x^{7}}{7}\right )\right )}{\left (-x^{7}\right )^{{6}/{7}}} \]

✓ Mathematica. Time used: 0.26 (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