ODE
\[ x y'(x)=y(x)-x \tan \left (\frac {y(x)}{x}\right ) \] ODE Classification
[[_homogeneous, `class A`], _dAlembert]
Book solution method
Homogeneous equation
Mathematica ✓
cpu = 0.0314434 (sec), leaf count = 16
\[\left \{\left \{y(x)\to x \sin ^{-1}\left (\frac {e^{c_1}}{x}\right )\right \}\right \}\]
Maple ✓
cpu = 0.012 (sec), leaf count = 17
\[ \left \{ -{\it \_C1}+\ln \left ( \sin \left ( {\frac {y \left ( x \right ) }{x}} \right ) \right ) +\ln \left ( x \right ) =0 \right \} \] Mathematica raw input
DSolve[x*y'[x] == -(x*Tan[y[x]/x]) + y[x],y[x],x]
Mathematica raw output
{{y[x] -> x*ArcSin[E^C[1]/x]}}
Maple raw input
dsolve(x*diff(y(x),x) = y(x)-x*tan(y(x)/x), y(x),'implicit')
Maple raw output
-_C1+ln(sin(y(x)/x))+ln(x) = 0