Internal problem ID [5496]
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. Problems for Review and Discovery. Page
53
Problem number: 1(a).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {x y^{\prime }+y-x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 13
dsolve(x*diff(y(x),x)+y(x)=x,y(x), singsol=all)
\[ y \relax (x ) = \frac {x}{2}+\frac {c_{1}}{x} \]
✓ Solution by Mathematica
Time used: 0.025 (sec). Leaf size: 17
DSolve[x*y'[x]+y[x]==x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x}{2}+\frac {c_1}{x} \\ \end{align*}