ODE No. 123

\[ x y'(x)-y(x)-x \sin \left (\frac {y(x)}{x}\right )=0 \]

✓ Mathematica : cpu = 0.0857616 (sec), leaf count = 32

DSolve[-(x*Sin[y[x]/x]) - y[x] + x*Derivative[1][y][x] == 0,y[x],x]

\[\left \{\left \{y(x)\to -x \cos ^{-1}(-\tanh (\log (x)+c_1))\right \},\left \{y(x)\to x \cos ^{-1}(-\tanh (\log (x)+c_1))\right \}\right \}\]

✓ Maple : cpu = 0.136 (sec), leaf count = 44

dsolve(x*diff(y(x),x)-x*sin(y(x)/x)-y(x) = 0,y(x))

\[y \left (x \right ) = \arctan \left (\frac {2 x c_{1}}{c_{1}^{2} x^{2}+1}, \frac {-c_{1}^{2} x^{2}+1}{c_{1}^{2} x^{2}+1}\right ) x\]