ODE
\[ y''(x)+2 \tan (x) y'(x)-y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.248334 (sec), leaf count = 37
\[\left \{\left \{y(x)\to c_2 \cos (x)+c_1 \sqrt {\sin ^2(x)}-c_2 \sqrt {\sin ^2(x)} \sin ^{-1}(\cos (x))\right \}\right \}\]
Maple ✓
cpu = 0.507 (sec), leaf count = 29
\[[y \left (x \right ) = \sin \left (x \right ) \textit {\_C1} +\textit {\_C2} \left (\ln \left (\sin \left (x \right )+i \cos \left (x \right )\right ) \sin \left (x \right )-i \cos \left (x \right )\right )]\] Mathematica raw input
DSolve[-y[x] + 2*Tan[x]*y'[x] + y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[2]*Cos[x] + C[1]*Sqrt[Sin[x]^2] - ArcSin[Cos[x]]*C[2]*Sqrt[Sin[x]^2]}}
Maple raw input
dsolve(diff(diff(y(x),x),x)+2*diff(y(x),x)*tan(x)-y(x) = 0, y(x))
Maple raw output
[y(x) = sin(x)*_C1+_C2*(ln(sin(x)+I*cos(x))*sin(x)-I*cos(x))]