\[ y'(x) \left (\sin (\alpha ) \left (y(x)^2-x^2\right )-2 x \cos (\alpha ) y(x)+\sqrt {x^2+y(x)^2} y(x)\right )+\cos (\alpha ) \left (y(x)^2-x^2\right )+2 x \sin (\alpha ) y(x)+x \sqrt {x^2+y(x)^2}=0 \] ✓ Mathematica : cpu = 96.4769 (sec), leaf count = 17681 \[ \text {Too large to display} \] ✓ Maple : cpu = 0.688 (sec), leaf count = 129
\[\left \{y \left (x \right ) = x \RootOf \left (c_{1}+\int _{}^{\textit {\_Z}}\frac {-\textit {\_a}^{3} \cos \left (2 \alpha \right )-\textit {\_a}^{3}-3 \textit {\_a}^{2} \sin \left (2 \alpha \right )+3 \textit {\_a} \cos \left (2 \alpha \right )-\textit {\_a} +\sin \left (2 \alpha \right )+\sqrt {2}\, \sqrt {\left (\textit {\_a}^{2}+1\right ) \left (\textit {\_a}^{2} \cos \left (2 \alpha \right )+\textit {\_a}^{2}+2 \textit {\_a} \sin \left (2 \alpha \right )-\cos \left (2 \alpha \right )+1\right )}}{\left (\textit {\_a}^{2}+1\right ) \left (\textit {\_a}^{2} \cos \left (2 \alpha \right )+\textit {\_a}^{2}+2 \textit {\_a} \sin \left (2 \alpha \right )-\cos \left (2 \alpha \right )+1\right )}d \textit {\_a} -\ln \left (x \right )\right )\right \}\]