\[ y'(x) \left (\sin (\alpha ) \left (y(x)^2-x^2\right )-2 x \cos (\alpha ) y(x)+\sqrt {x^2+y(x)^2} y(x)\right )+\cos (\alpha ) \left (y(x)^2-x^2\right )+2 x \sin (\alpha ) y(x)+x \sqrt {x^2+y(x)^2}=0 \] ✓ Mathematica : cpu = 91.9586 (sec), leaf count = 17681 \[ \text {Too large to display} \] ✓ Maple : cpu = 0.776 (sec), leaf count = 128
\[ \left \{ y \left ( x \right ) ={\it RootOf} \left ( -\ln \left ( x \right ) +\int ^{{\it \_Z}}\!-{\frac {1}{ \left ( {{\it \_a}}^{2}+1 \right ) \left ( \cos \left ( 2\,\alpha \right ) {{\it \_a}}^{2}+2\,{\it \_a}\,\sin \left ( 2\,\alpha \right ) +{{\it \_a}}^{2}-\cos \left ( 2\,\alpha \right ) +1 \right ) } \left ( \cos \left ( 2\,\alpha \right ) {{\it \_a}}^{3}+3\,\sin \left ( 2\,\alpha \right ) {{\it \_a}}^{2}+{{\it \_a}}^{3}-\sqrt { \left ( {{\it \_a}}^{2}+1 \right ) \left ( \cos \left ( 2\,\alpha \right ) {{\it \_a}}^{2}+2\,{\it \_a}\,\sin \left ( 2\,\alpha \right ) +{{\it \_a}}^{2}-\cos \left ( 2\,\alpha \right ) +1 \right ) }\sqrt {2}-3\,\cos \left ( 2\,\alpha \right ) {\it \_a}-\sin \left ( 2\,\alpha \right ) +{\it \_a} \right ) }{d{\it \_a}}+{\it \_C1} \right ) x \right \} \]