Internal problem ID [10909]
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(a).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime } x +2 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(diff(y(x),x$2)+2*x*diff(y(x),x)+2*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \operatorname {erfi}\left (x \right ) {\mathrm e}^{-x^{2}} c_{1} +c_{2} {\mathrm e}^{-x^{2}} \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 21
DSolve[y''[x]+2*x*y'[x]+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \operatorname {DawsonF}(x)+c_2 e^{-x^2} \\ \end{align*}