ODE
\[ x y'(x)+y(x)+2 x \sec (x y(x))=0 \] ODE Classification
[[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]
Book solution method
Exact equation, integrating factor
Mathematica ✓
cpu = 0.341702 (sec), leaf count = 19
\[\left \{\left \{y(x)\to -\frac {\sin ^{-1}\left (x^2-c_1\right )}{x}\right \}\right \}\]
Maple ✓
cpu = 0.407 (sec), leaf count = 16
\[\left [y \left (x \right ) = \frac {\arcsin \left (-x^{2}+\textit {\_C1} \right )}{x}\right ]\] Mathematica raw input
DSolve[2*x*Sec[x*y[x]] + y[x] + x*y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> -(ArcSin[x^2 - C[1]]/x)}}
Maple raw input
dsolve(x*diff(y(x),x)+y(x)+2*x*sec(x*y(x)) = 0, y(x))
Maple raw output
[y(x) = arcsin(-x^2+_C1)/x]