12.2.14 problem 14

Internal problem ID [1550]
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
Date solved : Monday, January 27, 2025 at 04:59:41 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }+2 y x&=x \,{\mathrm e}^{-x^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 19

dsolve(diff(y(x),x) +2*x*y(x)=x*exp(-x^2),y(x), singsol=all)
 

\[ y = \frac {\left (x^{2}+2 c_1 \right ) {\mathrm e}^{-x^{2}}}{2} \]

✓ Solution by Mathematica

Time used: 0.059 (sec). Leaf size: 24

DSolve[D[y[x],x] +2*x*y[x]==x*Exp[-x^2],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} e^{-x^2} \left (x^2+2 c_1\right ) \]