Internal problem ID [5933]
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]
\[ \boxed {2 x y+y^{\prime }=x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
dsolve(diff(y(x),x)+2*x*y(x)=x,y(x), singsol=all)
\[ y \left (x \right ) = \frac {1}{2}+{\mathrm e}^{-x^{2}} c_{1} \]
✓ Solution by Mathematica
Time used: 0.027 (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*}