2.338   ODE No. 338

\[ y'(x) \left (\sin (\alpha ) \left (y(x)^2-x^2\right )-2 x \cos (\alpha ) y(x)+\sqrt {x^2+y(x)^2} y(x)\right )+\cos (\alpha ) \left (y(x)^2-x^2\right )+2 x \sin (\alpha ) y(x)+x \sqrt {x^2+y(x)^2}=0 \] Mathematica : cpu = 61.416 (sec), leaf count = 17681


\[ \text {Too large to display} \] Maple : cpu = 0.857 (sec), leaf count = 127


\[y \relax (x ) = \RootOf \left (-\ln \relax (x )+\int _{}^{\textit {\_Z}}-\frac {\textit {\_a}^{3} \cos \left (2 \alpha \right )+3 \textit {\_a}^{2} \sin \left (2 \alpha \right )+\textit {\_a}^{3}-3 \textit {\_a} \cos \left (2 \alpha \right )-\sin \left (2 \alpha \right )+\sqrt {2}\, \sqrt {\left (\textit {\_a}^{2}+1\right ) \left (\textit {\_a}^{2} \cos \left (2 \alpha \right )+2 \textit {\_a} \sin \left (2 \alpha \right )+\textit {\_a}^{2}-\cos \left (2 \alpha \right )+1\right )}+\textit {\_a}}{\left (\textit {\_a}^{2}+1\right ) \left (\textit {\_a}^{2} \cos \left (2 \alpha \right )+2 \textit {\_a} \sin \left (2 \alpha \right )+\textit {\_a}^{2}-\cos \left (2 \alpha \right )+1\right )}d \textit {\_a} +c_{1}\right ) x\]