67.2.36 problem Problem 18(a)

Internal problem ID [13993]
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)
Date solved : Tuesday, January 28, 2025 at 06:11:12 AM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 0.044 (sec). Leaf size: 31

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

\[ y(x)\to \frac {1}{2} e^{-x^2} \left (\sqrt {\pi } c_1 \text {erfi}(x)+2 c_2\right ) \]