60.1.4 problem 4

Internal problem ID [10018]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 4
Date solved : Monday, January 27, 2025 at 06:18:24 PM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.002 (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: 0.066 (sec). Leaf size: 24

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

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