Internal problem ID [900]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. Linear first order. Section 2.1 Page 41
Problem number: 14.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime }+2 y x -x \,{\mathrm e}^{-x^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 18
dsolve(diff(y(x),x) +2*x*y(x)=x*exp(-x^2),y(x), singsol=all)
\[ y \relax (x ) = \left (\frac {x^{2}}{2}+c_{1}\right ) {\mathrm e}^{-x^{2}} \]
✓ Solution by Mathematica
Time used: 0.06 (sec). Leaf size: 24
DSolve[y'[x] +2*x*y[x]==x*Exp[-x^2],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} e^{-x^2} \left (x^2+2 c_1\right ) \\ \end{align*}