2.15 problem 15

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*}