Internal problem ID [2603]
Book: Differential equations with applications and historial notes, George F. Simmons,
1971
Section: Chapter 2, section 11, page 49
Problem number: 2(e).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime }+\cot \relax (x ) y-2 x \csc \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (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: 0.044 (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*}