Internal problem ID [5412]
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(i).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime }+y \cot \relax (x )-2 x \csc \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 14
dsolve(diff(y(x),x)+y(x)*cot(x)=2*x*csc(x),y(x), singsol=all)
\[ y \relax (x ) = \frac {x^{2}+c_{1}}{\sin \relax (x )} \]
✓ Solution by Mathematica
Time used: 0.072 (sec). Leaf size: 14
DSolve[y'[x]+y[x]*Cot[x]==2*x*Csc[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \left (x^2+c_1\right ) \csc (x) \\ \end{align*}