Internal problem ID [11937]
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]]
\[ \boxed {y^{\prime \prime }+2 x y^{\prime }+2 y=0} \]
✓ 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: 0.033 (sec). Leaf size: 31
DSolve[y''[x]+2*x*y'[x]+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} e^{-x^2} \left (\sqrt {\pi } c_1 \text {erfi}(x)+2 c_2\right ) \]