4.27.37 $y^{″}(x)+2\tan (x)y^{\prime }(x)+3y(x)=0$

ODE
$$y^{″}(x)+2\tan (x)y^{\prime }(x)+3y(x)=0$$ ODE Classification

[[_2nd_order, _with_linear_symmetries]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.104406 (sec), leaf count = 33

$$\left\{\{y(x)\to c_1{\cos }^3(x)-\frac{1}{3}{c}_2\sqrt{{\sin }^2(x)}(\cos (2x)+2)\}\right\}$$

Maple ✓
cpu = 0.129 (sec), leaf count = 25

$$\{y\left(x\right)=(-2\mathit{\_}\mathit{C}\mathit{2}{(\cos \left(x\right))}^2-\mathit{\_}\mathit{C}\mathit{2})\sin \left(x\right)+\mathit{\_}\mathit{C}\mathit{1}{(\cos \left(x\right))}^3\}$$ Mathematica raw input

DSolve[3*y[x] + 2*Tan[x]*y'[x] + y''[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> C[1]*Cos[x]^3 - (C[2]*(2 + Cos[2*x])*Sqrt[Sin[x]^2])/3}}

Maple raw input

dsolve(diff(diff(y(x),x),x)+2*diff(y(x),x)*tan(x)+3*y(x) = 0, y(x),'implicit')

Maple raw output

y(x) = (-2*_C2*cos(x)^2-_C2)*sin(x)+_C1*cos(x)^3