59.1.219 problem 222

Internal problem ID [9391]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 222
Date solved : Monday, January 27, 2025 at 06:02:14 PM
CAS classification : [_erf]

\begin{align*} y^{\prime \prime }+2 x y^{\prime }+4 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 25

dsolve(diff(y(x),x$2)+2*x*diff(y(x),x)+4*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.037 (sec). Leaf size: 51

DSolve[D[y[x],{x,2}]+2*x*D[y[x],x]+4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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