50.3.2 problem 1(b)

Internal problem ID [7826]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.4 First Order Linear Equations. Page 15
Problem number : 1(b)
Date solved : Monday, January 27, 2025 at 03:24:20 PM
CAS classification : [_separable]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

Time used: 0.059 (sec). Leaf size: 24

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

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