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 = 0.25753 (sec), leaf count = 19
\[\left \{\left \{y(x)\to 2 x \cot ^{-1}\left (\frac {e^{-c_1}}{x}\right )\right \}\right \}\]
Maple ✓
cpu = 0.07 (sec), leaf count = 44
\[\left [y \left (x \right ) = \arctan \left (\frac {2 x \textit {\_C1}}{\textit {\_C1}^{2} x^{2}+1}, -\frac {\textit {\_C1}^{2} x^{2}-1}{\textit {\_C1}^{2} x^{2}+1}\right ) x\right ]\] 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))
Maple raw output
[y(x) = arctan(2*x*_C1/(_C1^2*x^2+1),-(_C1^2*x^2-1)/(_C1^2*x^2+1))*x]