35.3.3 problem 3

Internal problem ID [6107]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 3. Linear First-Order Equations. page 403
Problem number : 3
Date solved : Monday, January 27, 2025 at 01:36:21 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }+2 y x -x \,{\mathrm e}^{-x^{2}}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 19

dsolve(diff(y(x),x)+2*x*y(x)-x*exp(-x^2)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.061 (sec). Leaf size: 24

DSolve[D[y[x],x]+2*x*y[x]-x*Exp[-x^2]==0,y[x],x,IncludeSingularSolutions -> True]
 

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