Internal problem ID [5418]
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]
\[ \boxed {x^{2} y^{\prime }+x y-2 x=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 13
dsolve([x^2*diff(y(x),x)+x*y(x)=2*x,y(1) = 1],y(x), singsol=all)
\[ y \left (x \right ) = \frac {2 x -1}{x} \]
✓ Solution by Mathematica
Time used: 0.037 (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*}