ODE
\[ x y'(x)=y(x)+x \sin \left (\frac {y(x)}{x}\right ) \] ODE Classification
[[_homogeneous, `class A`], _dAlembert]
Book solution method
Homogeneous equation
Mathematica ✓
cpu = 0.0554972 (sec), leaf count = 19
\[\left \{\left \{y(x)\to 2 x \cot ^{-1}\left (\frac {e^{-c_1}}{x}\right )\right \}\right \}\]
Maple ✓
cpu = 0.011 (sec), leaf count = 29
\[ \left \{ \ln \left ( \csc \left ( {\frac {y \left ( x \right ) }{x}} \right ) -\cot \left ( {\frac {y \left ( x \right ) }{x}} \right ) \right ) -\ln \left ( x \right ) -{\it \_C1}=0 \right \} \] Mathematica raw input
DSolve[x*y'[x] == x*Sin[y[x]/x] + y[x],y[x],x]
Mathematica raw output
{{y[x] -> 2*x*ArcCot[1/(E^C[1]*x)]}}
Maple raw input
dsolve(x*diff(y(x),x) = y(x)+x*sin(y(x)/x), y(x),'implicit')
Maple raw output
ln(csc(y(x)/x)-cot(y(x)/x))-ln(x)-_C1 = 0