2.1.2.2 ✓ Maple. Time used: 0.017 (sec). Leaf size: 28

ode:=2*x*tan(y(x))+(x-x^2*tan(y(x)))*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} x -\left (-\frac {\int _{}^{y}{\mathrm e}^{-\frac {\textit {\_a}}{2}} \cot \left (\textit {\_a} \right )d \textit {\_a}}{2}+c_1 \right ) {\mathrm e}^{\frac {y}{2}} = 0 \end{align*}

Maple trace

Methods for first order ODEs: 
--- Trying classification methods --- 
trying a quadrature 
trying 1st order linear 
trying Bernoulli 
trying separable 
trying inverse linear 
<- 1st order linear successful 
<- inverse linear successful
 

Maple step by step

\[ \begin {array}{lll} & {} & \textrm {Let's solve}\hspace {3pt} \\ {} & {} & 2 x \tan \left (y \left (x \right )\right )+\left (x -x^{2} \tan \left (y \left (x \right )\right )\right ) \left (\frac {d}{d x}y \left (x \right )\right )=0 \\ \bullet & {} & \textrm {Highest derivative means the order of the ODE is}\hspace {3pt} 1 \\ {} & {} & \frac {d}{d x}y \left (x \right ) \\ \bullet & {} & \textrm {Solve for the highest derivative}\hspace {3pt} \\ {} & {} & \frac {d}{d x}y \left (x \right )=-\frac {2 x \tan \left (y \left (x \right )\right )}{x -x^{2} \tan \left (y \left (x \right )\right )} \end {array} \]