Internal problem ID [3032]
Book: Elementary Differential equations, Chaundy, 1969
Section: Exercises 3, page 60
Problem number: 1(d).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime }+y \cot \left (x \right )=\tan \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 21
dsolve(diff(y(x),x)+y(x)*cot(x)=tan(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {-\sin \left (x \right )+\ln \left (\sec \left (x \right )+\tan \left (x \right )\right )+c_{1}}{\sin \left (x \right )} \]
✓ Solution by Mathematica
Time used: 0.046 (sec). Leaf size: 18
DSolve[y'[x]+y[x]*Cot[x]==Tan[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \csc (x) \text {arctanh}(\sin (x))+c_1 \csc (x)-1 \]