Internal problem ID [2523]
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]
Solve \begin {gather*} \boxed {y^{\prime }+\cot \relax (x ) y-\tan \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 21
dsolve(diff(y(x),x)+y(x)*cot(x)=tan(x),y(x), singsol=all)
\[ y \relax (x ) = \frac {-\sin \relax (x )+\ln \left (\sec \relax (x )+\tan \relax (x )\right )+c_{1}}{\sin \relax (x )} \]
✓ Solution by Mathematica
Time used: 0.057 (sec). Leaf size: 48
DSolve[y'[x]+y[x]*Cot[x]==Tan[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\csc (x) \left (\sin (x)+\log \left (\cos \left (\frac {x}{2}\right )-\sin \left (\frac {x}{2}\right )\right )-\log \left (\sin \left (\frac {x}{2}\right )+\cos \left (\frac {x}{2}\right )\right )-c_1\right ) \\ \end{align*}