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 = 0.251793 (sec), leaf count = 18
\[\{\{y(x)\to c_1 (2 \cos (2 x)+1) \sec (x)\}\}\]
Maple ✓
cpu = 0.07 (sec), leaf count = 18
\[\left [y \left (x \right ) = \frac {\textit {\_C1} \left (1+2 \cos \left (2 x \right )\right )}{\cos \left (x \right )}\right ]\] 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))
Maple raw output
[y(x) = _C1*(1+2*cos(2*x))/cos(x)]