5.15 problem 19

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]

Solve \begin {gather*} \boxed {y^{\prime }+2 y x -{\mathrm e}^{-x^{2}}=0} \end {gather*}

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)
 

\[ y \relax (x ) = \left (c_{1}+x \right ) {\mathrm e}^{-x^{2}} \]

Solution by Mathematica

Time used: 0.057 (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*}