4.5.12 \(x y'(x)+\tan (y(x))=0\)

ODE
\[ x y'(x)+\tan (y(x))=0 \] ODE Classification

[_separable]

Book solution method
Exact equation, integrating factor

Mathematica
cpu = 0.0193132 (sec), leaf count = 14

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

Maple
cpu = 0.006 (sec), leaf count = 11

\[ \left \{ \ln \relax (x ) +\ln \left (\sin \left (y \relax (x ) \right ) \right ) +{\it \_C1}=0 \right \} \] Mathematica raw input

DSolve[Tan[y[x]] + x*y'[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> ArcSin[E^C[1]/x]}}

Maple raw input

dsolve(x*diff(y(x),x)+tan(y(x)) = 0, y(x),'implicit')

Maple raw output

ln(x)+ln(sin(y(x)))+_C1 = 0