ODE
\[ y'(x) \left (\cot (x)-2 y(x)^2\right )=y(x)^3 \csc (x) \sec (x) \] ODE Classification
[`y=_G(x,y')`]
Book solution method
Change of Variable, new independent variable
Mathematica ✓
cpu = 0.744601 (sec), leaf count = 69
\[\left \{\left \{y(x)\to -\frac {i \sqrt {\cot (x)} \sqrt {W\left (-2 e^{-8 c_1} \tan (x)\right )}}{\sqrt {2}}\right \},\left \{y(x)\to \frac {i \sqrt {\cot (x)} \sqrt {W\left (-2 e^{-8 c_1} \tan (x)\right )}}{\sqrt {2}}\right \}\right \}\]
Maple ✗
cpu = 100.217 (sec), leaf count = 0 , could not solve
dsolve((cot(x)-2*y(x)^2)*diff(y(x),x) = y(x)^3*csc(x)*sec(x), y(x))
Mathematica raw input
DSolve[(Cot[x] - 2*y[x]^2)*y'[x] == Csc[x]*Sec[x]*y[x]^3,y[x],x]
Mathematica raw output
{{y[x] -> ((-I)*Sqrt[Cot[x]]*Sqrt[ProductLog[(-2*Tan[x])/E^(8*C[1])]])/Sqrt[2]}, {y[x] -> (I*Sqrt[Cot[x]]*Sqrt[ProductLog[(-2*Tan[x])/E^(8*C[1])]])/Sqrt[2]}}
Maple raw input
dsolve((cot(x)-2*y(x)^2)*diff(y(x),x) = y(x)^3*csc(x)*sec(x), y(x))
Maple raw output
dsolve((cot(x)-2*y(x)^2)*diff(y(x),x) = y(x)^3*csc(x)*sec(x), y(x))