59.1.721 problem 738

Internal problem ID [9893]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 738
Date solved : Sunday, March 30, 2025 at 02:49:00 PM
CAS classification : [_Hermite]

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

✓ Maple. Time used: 0.017 (sec). Leaf size: 37

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

\[ y = \left (x^{2}+1\right ) \left (c_1 \sqrt {\pi }\, \operatorname {erf}\left (\frac {\sqrt {2}\, x}{2}\right )+c_2 \right ) {\mathrm e}^{\frac {x^{2}}{2}}+\sqrt {2}\, c_1 x \]

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 35

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

\[ y(x)\to c_1 \operatorname {HermiteH}\left (-3,\frac {x}{\sqrt {2}}\right )+c_2 e^{\frac {x^2}{2}} \left (x^2+1\right ) \]

✗ Sympy

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

False