Internal problem ID [72]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.5. Linear first order equations. Page 56
Problem number: 19.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {\cot \relax (x ) y+y^{\prime }-\cos \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 17
dsolve(cot(x)*y(x)+diff(y(x),x) = cos(x),y(x), singsol=all)
\[ y \relax (x ) = \frac {-\frac {\cos \left (2 x \right )}{4}+c_{1}}{\sin \relax (x )} \]
✓ Solution by Mathematica
Time used: 0.044 (sec). Leaf size: 19
DSolve[Cot[x]*y[x]+y'[x] == Cos[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{2} \cos (x) \cot (x)+c_1 \csc (x) \\ \end{align*}