ODE
\[ b y(x)+y''(x)-2 \tan (x) y'(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0913941 (sec), leaf count = 54
\[\left \{\left \{y(x)\to \sec (x) \left (c_1 e^{-\sqrt {-b-1} x}+\frac {c_2 e^{\sqrt {-b-1} x}}{2 \sqrt {-b-1}}\right )\right \}\right \}\]
Maple ✓
cpu = 0.065 (sec), leaf count = 34
\[ \left \{ y \left ( x \right ) ={\frac {1}{\cos \left ( x \right ) } \left ( {\it \_C1}\,\sinh \left ( \sqrt {-b-1}x \right ) +{\it \_C2}\,\cosh \left ( \sqrt {-b-1}x \right ) \right ) } \right \} \] 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)