67.2.40 problem Problem 18(e)

Internal problem ID [13997]
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(e)
Date solved : Tuesday, January 28, 2025 at 06:11:20 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 16

dsolve(diff(y(x),x$2)+4*x*diff(y(x),x)+(2+4*x^2)*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 20

DSolve[D[y[x],{x,2}]+4*x*D[y[x],x]+(2+4*x^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x^2} (c_2 x+c_1) \]