4.10.29 $3y(x)y^{\prime }(x)+5\cot (x){\cos }^2(y(x))\cot (y(x))=0$

ODE
$$3y(x)y^{\prime }(x)+5\cot (x){\cos }^2(y(x))\cot (y(x))=0$$ ODE Classification

[_separable]

Book solution method
Separable ODE, Neither variable missing

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

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

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

$$\{\frac{(10\mathit{\_}\mathit{C}\mathit{1}+10\ln (\sin \left(x\right)))\cos \left(3y\left(x\right)\right)-3\sin \left(3y\left(x\right)\right)+(30\mathit{\_}\mathit{C}\mathit{1}+12y\left(x\right)+30\ln (\sin \left(x\right)))\cos \left(y\left(x\right)\right)-3\sin \left(y\left(x\right)\right)}{10\cos \left(3y\left(x\right)\right)+30\cos \left(y\left(x\right)\right)}=0\}$$ 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