4.27.38 $by(x)+y^{″}(x)-2\tan (x)y^{\prime }(x)=0$

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

[[_2nd_order, _with_linear_symmetries]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.0913941 (sec), leaf count = 54

$$\left\{\{y(x)\to \sec (x)(c_1{e}^{-\sqrt{-b-1}x}+\frac{c_2{e}^{\sqrt{-b-1}x}}{2\sqrt{-b-1}})\}\right\}$$

Maple ✓
cpu = 0.065 (sec), leaf count = 34

$$\{y\left(x\right)=\frac{1}{\cos \left(x\right)}(\mathit{\_}\mathit{C}\mathit{1}\sinh \left(\sqrt{-b-1}x\right)+\mathit{\_}\mathit{C}\mathit{2}\cosh \left(\sqrt{-b-1}x\right))\}$$ Mathematica raw input

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

Mathematica raw output

{{y[x] -> (C[1]/E^(Sqrt[-1 - b]*x) + (E^(Sqrt[-1 - b]*x)*C[2])/(2*Sqrt[-1 - b]))
*Sec[x]}}

Maple raw input

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

Maple raw output

y(x) = (_C1*sinh((-b-1)^(1/2)*x)+_C2*cosh((-b-1)^(1/2)*x))/cos(x)