3.16 problem 2(f)

Internal problem ID [5419]

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: 2(f).
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_separable]

Solve \begin {gather*} \boxed {x^{2} y^{\prime }+x y-2 x=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 1] \end {align*}

Solution by Maple

Time used: 0.006 (sec). Leaf size: 13

dsolve([x^2*diff(y(x),x)+x*y(x)=2*x,y(1) = 1],y(x), singsol=all)
 

\[ y \relax (x ) = \frac {2 x -1}{x} \]

Solution by Mathematica

Time used: 0.041 (sec). Leaf size: 12

DSolve[{x^2*y'[x]+x*y[x]==2*x,{y[1]==1}},y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to 2-\frac {1}{x} \\ \end{align*}