36.2.15 problem 15

Internal problem ID [6308]
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
Date solved : Monday, January 27, 2025 at 01:55:42 PM
CAS classification : [_separable]

\begin{align*} \left (x^{2}+1\right ) y^{\prime }+y x -x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 15

dsolve((x^2+1)*diff(y(x),x)+x*y(x)-x=0,y(x), singsol=all)
 

\[ y \left (x \right ) = 1+\frac {c_{1}}{\sqrt {x^{2}+1}} \]

✓ Solution by Mathematica

Time used: 0.035 (sec). Leaf size: 24

DSolve[(x^2+1)*D[y[x],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*}