Internal problem ID [2619]
Book: Differential equations with applications and historial notes, George F. Simmons,
1971
Section: Chapter 2, End of chapter, page 61
Problem number: 19.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime }+2 y x -{\mathrm e}^{-x^{2}}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
dsolve(diff(y(x),x)+2*x*y(x)=exp(-x^2),y(x), singsol=all)
\[ y \left (x \right ) = \left (x +c_{1} \right ) {\mathrm e}^{-x^{2}} \]
✓ Solution by Mathematica
Time used: 0.053 (sec). Leaf size: 17
DSolve[y'[x]+2*x*y[x]==Exp[-x^2],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-x^2} (x+c_1) \\ \end{align*}