Internal problem ID [7585]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 4.
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: 0.015 (sec). Leaf size: 18
dsolve(diff(y(x),x) + 2*x*y(x) - x*exp(-x^2)=0,y(x), singsol=all)
\[ y \relax (x ) = \left (\frac {x^{2}}{2}+c_{1}\right ) {\mathrm e}^{-x^{2}} \]
✓ Solution by Mathematica
Time used: 0.087 (sec). Leaf size: 24
DSolve[y'[x] + 2*x*y[x] - x*Exp[-x^2]==0,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*}