59.1.9 problem 9

Internal problem ID [9181]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 9
Date solved : Wednesday, March 05, 2025 at 07:37:29 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.043 (sec). Leaf size: 37

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

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

✓ Mathematica. Time used: 0.021 (sec). Leaf size: 35

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

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

✗ Sympy

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

False