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