12.1.3 problem 2(c)

Internal problem ID [1521]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 1, Introduction. Section 1.2 Page 14
Problem number : 2(c)
Date solved : Monday, January 27, 2025 at 04:58:45 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 14

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

\[ y = \frac {1}{2}+c_1 \,{\mathrm e}^{-x^{2}} \]

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 26

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

\begin{align*} y(x)\to \frac {1}{2}+c_1 e^{-x^2} \\ y(x)\to \frac {1}{2} \\ \end{align*}