4.10.29 \(3 y(x) y'(x)+5 \cot (x) \cos ^2(y(x)) \cot (y(x))=0\)

ODE
\[ 3 y(x) y'(x)+5 \cot (x) \cos ^2(y(x)) \cot (y(x))=0 \] ODE Classification

[_separable]

Book solution method
Separable ODE, Neither variable missing

Mathematica
cpu = 0.442068 (sec), leaf count = 29

\[\text {Solve}\left [c_1=40 \sin (x) e^{-\frac {3}{10} \left (\tan (y(x))-y(x) \sec ^2(y(x))\right )},y(x)\right ]\]

Maple
cpu = 0.028 (sec), leaf count = 64

\[ \left \{ {\frac { \left (10\,{\it \_C1}+10\,\ln \left (\sin \relax (x ) \right ) \right ) \cos \left (3\,y \relax (x ) \right ) -3\,\sin \left (3\,y \relax (x ) \right ) + \left (30\,{\it \_C1}+12\,y \relax (x ) +30\,\ln \left (\sin \relax (x ) \right ) \right ) \cos \left (y \relax (x ) \right ) -3\,\sin \left (y \relax (x ) \right ) }{10\,\cos \left (3\,y \relax (x ) \right ) +30\,\cos \left (y \relax (x ) \right ) }}=0 \right \} \] Mathematica raw input

DSolve[5*Cos[y[x]]^2*Cot[x]*Cot[y[x]] + 3*y[x]*y'[x] == 0,y[x],x]

Mathematica raw output

Solve[C[1] == (40*Sin[x])/E^((3*(Tan[y[x]] - Sec[y[x]]^2*y[x]))/10), y[x]]

Maple raw input

dsolve(3*y(x)*diff(y(x),x)+5*cot(x)*cot(y(x))*cos(y(x))^2 = 0, y(x),'implicit')

Maple raw output

((10*_C1+10*ln(sin(x)))*cos(3*y(x))-3*sin(3*y(x))+(30*_C1+12*y(x)+30*ln(sin(x)))
*cos(y(x))-3*sin(y(x)))/(10*cos(3*y(x))+30*cos(y(x))) = 0