3.1 problem 1(a)

Internal problem ID [5180]

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).
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_separable]

Solve \begin {gather*} \boxed {y^{\prime }+2 x y-x=0} \end {gather*}

Solution by Maple

Time used: 0.001 (sec). Leaf size: 14

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

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

Solution by Mathematica

Time used: 0.045 (sec). Leaf size: 26

DSolve[y'[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*}