49.3.1 problem 1(a)

Internal problem ID [7601]
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(a)
Date solved : Monday, January 27, 2025 at 03:07:09 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 14

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

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

✓ Solution by Mathematica

Time used: 0.031 (sec). Leaf size: 26

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

\begin{align*} y(x)\to \frac {1}{2}+c_1 e^{-x^2} \\ y(x)\to \frac {1}{2} \\ \end{align*}