4.1.33 \(y'(x)=2 y(x) \tan (x)+\sin (x)\)

ODE
\[ y'(x)=2 y(x) \tan (x)+\sin (x) \] ODE Classification

[_linear]

Book solution method
Linear ODE

Mathematica
cpu = 0.0182083 (sec), leaf count = 19

\[\left \{\left \{y(x)\to c_1 \sec ^2(x)-\frac {\cos (x)}{3}\right \}\right \}\]

Maple
cpu = 0.012 (sec), leaf count = 29

\[ \left \{ y \relax (x ) ={\frac {-\cos \left (3\,x \right ) -3\,\cos \relax (x ) +12\,{\it \_C1}}{6\,\cos \left (2\,x \right ) +6}} \right \} \] Mathematica raw input

DSolve[y'[x] == Sin[x] + 2*Tan[x]*y[x],y[x],x]

Mathematica raw output

{{y[x] -> -Cos[x]/3 + C[1]*Sec[x]^2}}

Maple raw input

dsolve(diff(y(x),x) = sin(x)+2*y(x)*tan(x), y(x),'implicit')

Maple raw output

y(x) = (-cos(3*x)-3*cos(x)+12*_C1)/(6*cos(2*x)+6)