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