Internal problem ID [2601]
Book: Differential equations with applications and historial notes, George F. Simmons,
1971
Section: Chapter 2, section 11, page 49
Problem number: 2(c).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {\left (x^{2}+1\right ) y^{\prime }+2 y x -\cot \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 17
dsolve((1+x^2)*diff(y(x),x)+2*x*y(x)=cot(x),y(x), singsol=all)
\[ y \relax (x ) = \frac {\ln \left (\sin \relax (x )\right )+c_{1}}{x^{2}+1} \]
✓ Solution by Mathematica
Time used: 0.065 (sec). Leaf size: 19
DSolve[(1+x^2)*y'[x]+2*x*y[x]==Cot[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\log (\sin (x))+c_1}{x^2+1} \\ \end{align*}