#### 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 = 72.6815 (sec), leaf count = 17681 $\text {Too large to display}$ Maple : cpu = 0.547 (sec), leaf count = 128

$\left \{ y \left ( x \right ) ={\it RootOf} \left ( -\ln \left ( x \right ) +\int ^{{\it \_Z}}\!-{\frac {1}{ \left ( {{\it \_a}}^{2}+1 \right ) \left ( {{\it \_a}}^{2}\cos \left ( 2\,\alpha \right ) +2\,{\it \_a}\,\sin \left ( 2\,\alpha \right ) +{{\it \_a}}^{2}-\cos \left ( 2\,\alpha \right ) +1 \right ) } \left ( {{\it \_a}}^{3}\cos \left ( 2\,\alpha \right ) +3\,{{\it \_a}}^{2}\sin \left ( 2\,\alpha \right ) +{{\it \_a}}^{3}-3\,{\it \_a}\,\cos \left ( 2\,\alpha \right ) -\sin \left ( 2\,\alpha \right ) -\sqrt {2}\sqrt { \left ( {{\it \_a}}^{2}+1 \right ) \left ( {{\it \_a}}^{2}\cos \left ( 2\,\alpha \right ) +2\,{\it \_a}\,\sin \left ( 2\,\alpha \right ) +{{\it \_a}}^{2}-\cos \left ( 2\,\alpha \right ) +1 \right ) }+{\it \_a} \right ) }{d{\it \_a}}+{\it \_C1} \right ) x \right \}$