78.18.2 problem 2 (a)

Internal problem ID [18414]
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 : Tuesday, January 28, 2025 at 11:49:38 AM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 22

dsolve(diff(y(x),x$2)+x*diff(y(x),x)+y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

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

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

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