Internal problem ID [5405]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }+x y-x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 14
dsolve(diff(y(x),x)+x*y(x)=x,y(x), singsol=all)
\[ y \relax (x ) = 1+{\mathrm e}^{-\frac {x^{2}}{2}} c_{1} \]
✓ Solution by Mathematica
Time used: 0.056 (sec). Leaf size: 24
DSolve[y'[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*}