Internal problem ID [3041]
Book: Elementary Differential equations, Chaundy, 1969
Section: Exercises 3, page 60
Problem number: 3(b).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {\cot \left (x \right ) y^{\prime }+y=\tan \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve(cot(x)*diff(y(x),x)+y(x)=tan(x),y(x), singsol=all)
\[ y \left (x \right ) = \left (\frac {\sin \left (x \right )^{3}}{2 \cos \left (x \right )^{2}}+\frac {\sin \left (x \right )}{2}-\frac {\ln \left (\sec \left (x \right )+\tan \left (x \right )\right )}{2}+c_{1} \right ) \cos \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.071 (sec). Leaf size: 25
DSolve[Cot[x]*y'[x]+y[x]==Tan[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} (\cos (x) (-\text {arctanh}(\sin (x)))+\tan (x)+2 c_1 \cos (x)) \]