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 = 0.144565 (sec), leaf count = 36
\[\left \{\left \{y(x)\to c_1 \sqrt {\sin ^2(x)}+c_2 \left (\cos (x)-\sqrt {\sin ^2(x)} \sin ^{-1}(\cos (x))\right )\right \}\right \}\]
Maple ✓
cpu = 0.134 (sec), leaf count = 28
\[ \left \{ y \left ( x \right ) =\sin \left ( x \right ) \ln \left ( \sin \left ( x \right ) +i\cos \left ( x \right ) \right ) {\it \_C2}-i\cos \left ( x \right ) {\it \_C2}+{\it \_C1}\,\sin \left ( x \right ) \right \} \] Mathematica raw input
DSolve[-y[x] + 2*Tan[x]*y'[x] + y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[1]*Sqrt[Sin[x]^2] + C[2]*(Cos[x] - ArcSin[Cos[x]]*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),'implicit')
Maple raw output
y(x) = sin(x)*ln(sin(x)+I*cos(x))*_C2-I*cos(x)*_C2+_C1*sin(x)