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 = 0.343621 (sec), leaf count = 16
\[\left \{\left \{y(x)\to x \sin ^{-1}\left (\frac {e^{c_1}}{x}\right )\right \}\right \}\]
Maple ✓
cpu = 0.028 (sec), leaf count = 14
\[\left [y \left (x \right ) = \arcsin \left (\frac {1}{x \textit {\_C1}}\right ) x\right ]\] 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))
Maple raw output
[y(x) = arcsin(1/x/_C1)*x]