Internal problem ID [10917]
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).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
\[ \boxed {x y^{\prime \prime }+x^{2} y^{\prime }+2 x y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 42
dsolve(x*diff(y(x),x$2)+x^2*diff(y(x),x)+2*x*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} x \,{\mathrm e}^{-\frac {x^{2}}{2}}+c_{2} \left (i {\mathrm e}^{-\frac {x^{2}}{2}} \operatorname {erf}\left (\frac {i \sqrt {2}\, x}{2}\right ) \sqrt {2}\, \sqrt {\pi }\, x +2\right ) \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 44
DSolve[x*y''[x]+x^2*y'[x]+2*x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {2} c_2 x \operatorname {DawsonF}\left (\frac {x}{\sqrt {2}}\right )+\sqrt {2} c_1 e^{-\frac {x^2}{2}} x+c_2 \\ \end{align*}