59.1.299 problem 302

Internal problem ID [9471]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 302
Date solved : Sunday, March 30, 2025 at 02:35:40 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-2 x y^{\prime }+x^{2} y&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 20

ode:=diff(diff(y(x),x),x)-2*x*diff(y(x),x)+x^2*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{\frac {x^{2}}{2}} \left (c_1 \cos \left (x \right )+c_2 \sin \left (x \right )\right ) \]

✓ Mathematica. Time used: 0.033 (sec). Leaf size: 39

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

\[ y(x)\to \frac {1}{2} e^{\frac {1}{2} x (x-2 i)} \left (2 c_1-i c_2 e^{2 i x}\right ) \]

✗ Sympy

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

False