67.2.44 problem Problem 18(i)

Internal problem ID [14001]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 4, Second and Higher Order Linear Differential Equations. Problems page 221
Problem number : Problem 18(i)
Date solved : Tuesday, January 28, 2025 at 06:11:25 AM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

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

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 37

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

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

✓ Solution by Mathematica

Time used: 0.050 (sec). Leaf size: 69

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

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