Internal problem ID [5937]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {2 x y+y^{\prime }=x \,{\mathrm e}^{-x^{2}}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve(diff(y(x),x)+2*x*y(x)=x*exp(-x^2),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (x^{2}+2 c_{1} \right ) {\mathrm e}^{-x^{2}}}{2} \]
✓ Solution by Mathematica
Time used: 0.057 (sec). Leaf size: 24
DSolve[y'[x]+2*x*y[x]==x*Exp[-x^2],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} e^{-x^2} \left (x^2+2 c_1\right ) \]