\[ \text {Global$\grave { }$y}'(\text {Global$\grave { }$x}) \left (\sin (\text {Global$\grave { }$alpha}) \left (\text {Global$\grave { }$y}(\text {Global$\grave { }$x})^2-\text {Global$\grave { }$x}^2\right )-2 \text {Global$\grave { }$x} \cos (\text {Global$\grave { }$alpha}) \text {Global$\grave { }$y}(\text {Global$\grave { }$x})+\sqrt {\text {Global$\grave { }$x}^2+\text {Global$\grave { }$y}(\text {Global$\grave { }$x})^2} \text {Global$\grave { }$y}(\text {Global$\grave { }$x})\right )+\cos (\text {Global$\grave { }$alpha}) \left (\text {Global$\grave { }$y}(\text {Global$\grave { }$x})^2-\text {Global$\grave { }$x}^2\right )+2 \text {Global$\grave { }$x} \sin (\text {Global$\grave { }$alpha}) \text {Global$\grave { }$y}(\text {Global$\grave { }$x})+\text {Global$\grave { }$x} \sqrt {\text {Global$\grave { }$x}^2+\text {Global$\grave { }$y}(\text {Global$\grave { }$x})^2}=0 \] ✓ Mathematica : cpu = 92.171 (sec), leaf count = 17681
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✓ Maple : cpu = 0.925 (sec), leaf count = 129
\[ \left \{ y \left ( x \right ) ={\it RootOf} \left ( -\ln \left ( x \right ) +\int ^{{\it \_Z}}\!{\frac {1}{ \left ( {{\it \_a}}^{2}+1 \right ) \left ( \cos \left ( 2\,\alpha \right ) {{\it \_a}}^{2}+2\,{\it \_a}\,\sin \left ( 2\,\alpha \right ) +{{\it \_a}}^{2}-\cos \left ( 2\,\alpha \right ) +1 \right ) } \left ( -\cos \left ( 2\,\alpha \right ) {{\it \_a}}^{3}-3\,\sin \left ( 2\,\alpha \right ) {{\it \_a}}^{2}-{{\it \_a}}^{3}+\sqrt {2}\sqrt { \left ( {{\it \_a}}^{2}+1 \right ) \left ( \cos \left ( 2\,\alpha \right ) {{\it \_a}}^{2}+2\,{\it \_a}\,\sin \left ( 2\,\alpha \right ) +{{\it \_a}}^{2}-\cos \left ( 2\,\alpha \right ) +1 \right ) }+3\,\cos \left ( 2\,\alpha \right ) {\it \_a}+\sin \left ( 2\,\alpha \right ) -{\it \_a} \right ) }{d{\it \_a}}+{\it \_C1} \right ) x \right \} \]