Internal problem ID [5413]
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: 1(j).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y-x +x y \cot \relax (x )+x y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 21
dsolve(y(x)-x+x*y(x)*cot(x)+x*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {-x \cos \relax (x )+\sin \relax (x )+c_{1}}{x \sin \relax (x )} \]
✓ Solution by Mathematica
Time used: 0.077 (sec). Leaf size: 21
DSolve[y[x]-x+x*y[x]*Cot[x]+x*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {-x \cot (x)+c_1 \csc (x)+1}{x} \\ \end{align*}