ODE
\[ y'(x)=2 (y(x) \tan (2 x)+\sec (2 x)+1) \] ODE Classification
[_linear]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.180867 (sec), leaf count = 20
\[\{\{y(x)\to \sec (2 x) (2 x+\sin (2 x)+c_1)\}\}\]
Maple ✓
cpu = 0.345 (sec), leaf count = 48
\[\left [y \left (x \right ) = \sqrt {1+\tan ^{2}\left (2 x \right )}\, \textit {\_C1} +\sqrt {2}\, \sqrt {\frac {1}{\cos \left (4 x \right )+1}}\, \cos \left (2 x \right ) \left (2 x +\sin \left (2 x \right )\right ) \sqrt {1+\tan ^{2}\left (2 x \right )}\right ]\] Mathematica raw input
DSolve[y'[x] == 2*(1 + Sec[2*x] + Tan[2*x]*y[x]),y[x],x]
Mathematica raw output
{{y[x] -> Sec[2*x]*(2*x + C[1] + Sin[2*x])}}
Maple raw input
dsolve(diff(y(x),x) = 2+2*sec(2*x)+2*y(x)*tan(2*x), y(x))
Maple raw output
[y(x) = (1+tan(2*x)^2)^(1/2)*_C1+(1/cos(2*x)^2)^(1/2)*cos(2*x)*(2*x+sin(2*x))*(1+tan(2*x)^2)^(1/2)]