78.18.2 problem 2 (a)

Internal problem ID [18343]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 5. Power Series Solutions and Special Functions. Section 28. Second Order Linear Equations. Ordinary Points. Problems at page 217
Problem number : 2 (a)
Date solved : Monday, March 31, 2025 at 05:25:59 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 22

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

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

✓ Mathematica. Time used: 0.049 (sec). Leaf size: 41

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

\[ y(x)\to \frac {1}{2} e^{-\frac {x^2}{2}} \left (\sqrt {2 \pi } c_1 \text {erfi}\left (\frac {x}{\sqrt {2}}\right )+2 c_2\right ) \]

✗ Sympy

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

False