4.9.14 \(\left (1-4 \cos ^2(x)\right ) y'(x)=y(x) \left (4 \cos ^2(x)+1\right ) \tan (x)\)

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

\[ \left \{ y \relax (x ) ={\frac {2\,{\it \_C1}\,\cos \left (2\,x \right ) +{\it \_C1}}{\cos \relax (x ) }} \right \} \] 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)