##### 4.25.47 $$-2 \tan (a) y'(x)+\csc ^2(a) y(x)+y''(x)=0$$

ODE
$-2 \tan (a) y'(x)+\csc ^2(a) y(x)+y''(x)=0$ ODE Classiﬁcation

[[_2nd_order, _missing_x]]

Book solution method
TO DO

Mathematica
cpu = 0.17729 (sec), leaf count = 58

$\left \{\left \{y(x)\to c_1 e^{x \left (\tan (a)-\sqrt {\tan ^2(a)-\csc ^2(a)}\right )}+c_2 e^{x \left (\tan (a)+\sqrt {\tan ^2(a)-\csc ^2(a)}\right )}\right \}\right \}$

Maple
cpu = 0.295 (sec), leaf count = 109

$\left [y \left (x \right ) = \textit {\_C1} \,{\mathrm e}^{-\frac {\left (\cos \left (a \right ) \left (\sin ^{2}\left (a \right )\right )-\sqrt {\left (\cos ^{2}\left (a \right )\right ) \left (\sin ^{4}\left (a \right )\right )-\left (\sin ^{4}\left (a \right )\right )+2 \left (\sin ^{2}\left (a \right )\right )-1}\right ) x}{\left (\sin ^{2}\left (a \right )-1\right ) \sin \left (a \right )}}+\textit {\_C2} \,{\mathrm e}^{-\frac {\left (\cos \left (a \right ) \left (\sin ^{2}\left (a \right )\right )+\sqrt {\left (\cos ^{2}\left (a \right )\right ) \left (\sin ^{4}\left (a \right )\right )-\left (\sin ^{4}\left (a \right )\right )+2 \left (\sin ^{2}\left (a \right )\right )-1}\right ) x}{\left (\sin ^{2}\left (a \right )-1\right ) \sin \left (a \right )}}\right ]$ Mathematica raw input

DSolve[Csc[a]^2*y[x] - 2*Tan[a]*y'[x] + y''[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> E^(x*(Tan[a] - Sqrt[-Csc[a]^2 + Tan[a]^2]))*C[1] + E^(x*(Tan[a] + Sqrt
[-Csc[a]^2 + Tan[a]^2]))*C[2]}}

Maple raw input

dsolve(diff(diff(y(x),x),x)-2*diff(y(x),x)*tan(a)+y(x)*csc(a)^2 = 0, y(x))

Maple raw output

[y(x) = _C1*exp(-(cos(a)*sin(a)^2-(cos(a)^2*sin(a)^4-sin(a)^4+2*sin(a)^2-1)^(1/2
))/(sin(a)^2-1)/sin(a)*x)+_C2*exp(-(cos(a)*sin(a)^2+(cos(a)^2*sin(a)^4-sin(a)^4+
2*sin(a)^2-1)^(1/2))/(sin(a)^2-1)/sin(a)*x)]