26.5.15 problem 19

Internal problem ID [4289]
Book : Differential equations with applications and historial notes, George F. Simmons. Second edition. 1971
Section : Chapter 2, End of chapter, page 61
Problem number : 19
Date solved : Monday, January 27, 2025 at 08:49:14 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.001 (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: 0.060 (sec). Leaf size: 17

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

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