15.6.3 problem 3

Internal problem ID [2960]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 10, page 41
Problem number : 3
Date solved : Monday, January 27, 2025 at 07:04:29 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 16

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

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

✓ Solution by Mathematica

Time used: 0.066 (sec). Leaf size: 19

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

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