Internal problem ID [4456]
Book: Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson
2018.
Section: Chapter 2, First order differential equations. Section 2.3, Linear equations. Exercises. page
54
Problem number: 15.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\left (x^{2}+1\right ) y^{\prime }+y x -x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve((x^2+1)*diff(y(x),x)+x*y(x)-x=0,y(x), singsol=all)
\[ y \relax (x ) = 1+\frac {c_{1}}{\sqrt {x^{2}+1}} \]
✓ Solution by Mathematica
Time used: 0.051 (sec). Leaf size: 24
DSolve[(x^2+1)*y'[x]+x*y[x]-x==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 1+\frac {c_1}{\sqrt {x^2+1}} \\ y(x)\to 1 \\ \end{align*}