##### 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 = 0.842774 (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 = 0.353 (sec), leaf count = 60

$\left [\frac {-3 \tan \left (y \left (x \right )\right ) \cos \left (2 y \left (x \right )\right )+10 \ln \left (\sin \left (x \right )\right ) \cos \left (2 y \left (x \right )\right )+10 \textit {\_C1} \cos \left (2 y \left (x \right )\right )-3 \tan \left (y \left (x \right )\right )+10 \ln \left (\sin \left (x \right )\right )+10 \textit {\_C1} +6 y \left (x \right )}{10 \cos \left (2 y \left (x \right )\right )+10} = 0\right ]$ 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))

Maple raw output

[1/10*(-3*tan(y(x))*cos(2*y(x))+10*ln(sin(x))*cos(2*y(x))+10*_C1*cos(2*y(x))-3*t
an(y(x))+10*ln(sin(x))+10*_C1+6*y(x))/(cos(2*y(x))+1) = 0]