49.3.5 problem 1(e)

Internal problem ID [7605]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 1. Introduction– Linear equations of First Order. Page 45
Problem number : 1(e)
Date solved : Monday, January 27, 2025 at 03:07:16 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }+2 y x&=x \,{\mathrm e}^{-x^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 19

dsolve(diff(y(x),x)+2*x*y(x)=x*exp(-x^2),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.068 (sec). Leaf size: 24

DSolve[D[y[x],x]+2*x*y[x]==x*Exp[-x^2],y[x],x,IncludeSingularSolutions -> True]
 

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