ODE
\[ y''(x)+2 \tan (x) y'(x)+3 y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.104406 (sec), leaf count = 33
\[\left \{\left \{y(x)\to c_1 \cos ^3(x)-\frac {1}{3} c_2 \sqrt {\sin ^2(x)} (\cos (2 x)+2)\right \}\right \}\]
Maple ✓
cpu = 0.129 (sec), leaf count = 25
\[ \left \{ y \left ( x \right ) = \left ( -2\,{\it \_C2}\, \left ( \cos \left ( x \right ) \right ) ^{2}-{\it \_C2} \right ) \sin \left ( x \right ) +{\it \_C1}\, \left ( \cos \left ( x \right ) \right ) ^{3} \right \} \] Mathematica raw input
DSolve[3*y[x] + 2*Tan[x]*y'[x] + y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[1]*Cos[x]^3 - (C[2]*(2 + Cos[2*x])*Sqrt[Sin[x]^2])/3}}
Maple raw input
dsolve(diff(diff(y(x),x),x)+2*diff(y(x),x)*tan(x)+3*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = (-2*_C2*cos(x)^2-_C2)*sin(x)+_C1*cos(x)^3