59.1.313 problem 318

Internal problem ID [9485]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 318
Date solved : Sunday, March 30, 2025 at 02:35:58 PM
CAS classification : [_Hermite]

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

✓ Maple. Time used: 0.010 (sec). Leaf size: 42

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

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

✓ Mathematica. Time used: 0.203 (sec). Leaf size: 43

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

\[ y(x)\to \left (x^2-1\right ) \left (c_2 \int _1^x\frac {e^{\frac {K[1]^2}{2}}}{\left (K[1]^2-1\right )^2}dK[1]+c_1\right ) \]

✗ 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