ODE
\[ \left (1-4 \cos ^2(x)\right ) y'(x)=y(x) \left (4 \cos ^2(x)+1\right ) \tan (x) \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.0583134 (sec), leaf count = 18
\[\left \{\left \{y(x)\to c_1 (2 \cos (2 x)+1) \sec (x)\right \}\right \}\]
Maple ✓
cpu = 0.06 (sec), leaf count = 18
\[ \left \{ y \left ( x \right ) ={\frac {2\,{\it \_C1}\,\cos \left ( 2\,x \right ) +{\it \_C1}}{\cos \left ( x \right ) }} \right \} \] Mathematica raw input
DSolve[(1 - 4*Cos[x]^2)*y'[x] == (1 + 4*Cos[x]^2)*Tan[x]*y[x],y[x],x]
Mathematica raw output
{{y[x] -> C[1]*(1 + 2*Cos[2*x])*Sec[x]}}
Maple raw input
dsolve((1-4*cos(x)^2)*diff(y(x),x) = tan(x)*(1+4*cos(x)^2)*y(x), y(x),'implicit')
Maple raw output
y(x) = (2*_C1*cos(2*x)+_C1)/cos(x)