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 = 0.0159926 (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 = 0.08 (sec), leaf count = 99
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{-{\frac {x}{ \left ( \sin \left ( a \right ) \right ) ^{3}-\sin \left ( a \right ) } \left ( \cos \left ( a \right ) \left ( \sin \left ( a \right ) \right ) ^{2}-\sqrt {-1+ \left ( \left ( \cos \left ( a \right ) \right ) ^{2}-1 \right ) \left ( \sin \left ( a \right ) \right ) ^{4}+2\, \left ( \sin \left ( a \right ) \right ) ^{2}} \right ) }}}+{\it \_C2}\,{{\rm e}^{-{\frac {x}{ \left ( \sin \left ( a \right ) \right ) ^{3}-\sin \left ( a \right ) } \left ( \cos \left ( a \right ) \left ( \sin \left ( a \right ) \right ) ^{2}+\sqrt {-1+ \left ( \left ( \cos \left ( a \right ) \right ) ^{2}-1 \right ) \left ( \sin \left ( a \right ) \right ) ^{4}+2\, \left ( \sin \left ( a \right ) \right ) ^{2}} \right ) }}} \right \} \] 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),'implicit')
Maple raw output
y(x) = _C1*exp(-(cos(a)*sin(a)^2-(-1+(cos(a)^2-1)*sin(a)^4+2*sin(a)^2)^(1/2))*x/(sin(a)^3-sin(a)))+_C2*exp(-(cos(a)*sin(a)^2+(-1+(cos(a)^2-1)*sin(a)^4+2*sin(a)^2)^(1/2))*x/(sin(a)^3-sin(a)))