\[ y'(x) \left (\sin (\alpha ) \left (y(x)^2-x^2\right )-2 x \cos (\alpha ) y(x)+\sqrt {x^2+y(x)^2} y(x)\right )+\cos (\alpha ) \left (y(x)^2-x^2\right )+2 x \sin (\alpha ) y(x)+x \sqrt {x^2+y(x)^2}=0 \] ✓ Mathematica : cpu = 102.095 (sec), leaf count = 1
\[\text {$\$$Aborted}\]
✓ Maple : cpu = 1.892 (sec), leaf count = 129
\[ \left \{ y \left ( x \right ) ={\it RootOf} \left ( -\ln \left ( x \right ) +\int ^{{\it \_Z}}\!{\frac {1}{ \left ( {{\it \_a}}^{2}+1 \right ) \left ( \cos \left ( 2\,\alpha \right ) {{\it \_a}}^{2}+2\,{\it \_a}\,\sin \left ( 2\,\alpha \right ) +{{\it \_a}}^{2}-\cos \left ( 2\,\alpha \right ) +1 \right ) } \left ( -\cos \left ( 2\,\alpha \right ) {{\it \_a}}^{3}-3\,\sin \left ( 2\,\alpha \right ) {{\it \_a}}^{2}-{{\it \_a}}^{3}+\sqrt {2}\sqrt { \left ( {{\it \_a}}^{2}+1 \right ) \left ( \cos \left ( 2\,\alpha \right ) {{\it \_a}}^{2}+2\,{\it \_a}\,\sin \left ( 2\,\alpha \right ) +{{\it \_a}}^{2}-\cos \left ( 2\,\alpha \right ) +1 \right ) }+3\,\cos \left ( 2\,\alpha \right ) {\it \_a}+\sin \left ( 2\,\alpha \right ) -{\it \_a} \right ) }{d{\it \_a}}+{\it \_C1} \right ) x \right \} \]