4.5.7 \(x y'(x)+y(x)+2 x \sec (x y(x))=0\)

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 = 0.0620316 (sec), leaf count = 19

\[\left \{\left \{y(x)\to -\frac {\sin ^{-1}\left (x^2-c_1\right )}{x}\right \}\right \}\]

Maple
cpu = 0.338 (sec), leaf count = 15

\[ \left \{ \sin \left (xy \relax (x ) \right ) +{x}^{2}-{\it \_C1}=0 \right \} \] 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),'implicit')

Maple raw output

sin(x*y(x))+x^2-_C1 = 0