\[ \boxed { \left ( y \left ( x \right ) \sqrt { \left ( y \left ( x \right ) \right ) ^{2}+{x}^{2}}+ \left ( \left ( y \left ( x \right ) \right ) ^{2}-{x}^{2} \right ) \sin \left ( \alpha \right ) -2\,xy \left ( x \right ) \cos \left ( \alpha \right ) \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +x\sqrt { \left ( y \left ( x \right ) \right ) ^{2}+{x}^{2}}+2\,xy \left ( x \right ) \sin \left ( \alpha \right ) + \left ( \left ( y \left ( x \right ) \right ) ^{2}-{x}^{2} \right ) \cos \left ( \alpha \right ) =0} \]
Mathematica: cpu = 77.787378 (sec), leaf count = 17681 \[ \left \{\left \{y(x)\to -\frac {1}{2} e^{c_1} \sin (\alpha )-\frac {1}{2} \sqrt {e^{2 c_1} \sin ^2(\alpha )+\frac {1}{6} \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+\frac {1}{2} \left (-4 x^2+4 e^{c_1} \cos (\alpha ) x+e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right )+\frac {\sqrt [3]{2 \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^3-144 x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+72 e^{2 c_1} x \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+432 e^{2 c_1} x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \sin ^2(\alpha )+216 e^{2 c_1} x^2 \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ){}^2+\sqrt {\left (2 \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^3-144 x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+72 e^{2 c_1} x \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+432 e^{2 c_1} x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \sin ^2(\alpha )+216 e^{2 c_1} x^2 \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ){}^2\right ){}^2-4 \left (24 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) x^2+24 e^{2 c_1} \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) x+\left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^2\right ){}^3}}}{6 \sqrt [3]{2}}+\frac {128 x^4-256 e^{c_1} \cos (\alpha ) x^3-96 e^{2 c_1} x^2+96 e^{2 c_1} \cos (2 \alpha ) x^2+48 e^{3 c_1} \cos (\alpha ) x-16 e^{3 c_1} \cos (3 \alpha ) x+3 e^{4 c_1}+4 e^{4 c_1} \cos (2 \alpha )+e^{4 c_1} \cos (4 \alpha )}{6\ 2^{2/3} \sqrt [3]{2 \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^3-144 x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+72 e^{2 c_1} x \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+432 e^{2 c_1} x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \sin ^2(\alpha )+216 e^{2 c_1} x^2 \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ){}^2+\sqrt {\left (2 \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^3-144 x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+72 e^{2 c_1} x \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+432 e^{2 c_1} x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \sin ^2(\alpha )+216 e^{2 c_1} x^2 \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ){}^2\right ){}^2-4 \left (24 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) x^2+24 e^{2 c_1} \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) x+\left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^2\right ){}^3}}}}-\frac {1}{2} \sqrt {2 e^{2 c_1} \sin ^2(\alpha )+\frac {2}{3} \left (-4 x^2+4 e^{c_1} \cos (\alpha ) x+e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right )-\frac {\sqrt [3]{2 \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^3-144 x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+72 e^{2 c_1} x \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+432 e^{2 c_1} x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \sin ^2(\alpha )+216 e^{2 c_1} x^2 \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ){}^2+\sqrt {\left (2 \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^3-144 x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+72 e^{2 c_1} x \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+432 e^{2 c_1} x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \sin ^2(\alpha )+216 e^{2 c_1} x^2 \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ){}^2\right ){}^2-4 \left (24 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) x^2+24 e^{2 c_1} \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) x+\left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^2\right ){}^3}}}{6 \sqrt [3]{2}}-\frac {128 x^4-256 e^{c_1} \cos (\alpha ) x^3-96 e^{2 c_1} x^2+96 e^{2 c_1} \cos (2 \alpha ) x^2+48 e^{3 c_1} \cos (\alpha ) x-16 e^{3 c_1} \cos (3 \alpha ) x+3 e^{4 c_1}+4 e^{4 c_1} \cos (2 \alpha )+e^{4 c_1} \cos (4 \alpha )}{6\ 2^{2/3} \sqrt [3]{2 \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^3-144 x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+72 e^{2 c_1} x \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+432 e^{2 c_1} x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \sin ^2(\alpha )+216 e^{2 c_1} x^2 \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ){}^2+\sqrt {\left (2 \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^3-144 x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+72 e^{2 c_1} x \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+432 e^{2 c_1} x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \sin ^2(\alpha )+216 e^{2 c_1} x^2 \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ){}^2\right ){}^2-4 \left (24 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) x^2+24 e^{2 c_1} \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) x+\left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^2\right ){}^3}}}-\frac {-8 e^{3 c_1} \sin ^3(\alpha )+4 e^{c_1} \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ) \sin (\alpha )+8 e^{c_1} x \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right )}{4 \sqrt {e^{2 c_1} \sin ^2(\alpha )+\frac {1}{6} \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+\frac {1}{2} \left (-4 x^2+4 e^{c_1} \cos (\alpha ) x+e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right )+\frac {\sqrt [3]{2 \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^3-144 x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+72 e^{2 c_1} x \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+432 e^{2 c_1} x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \sin ^2(\alpha )+216 e^{2 c_1} x^2 \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ){}^2+\sqrt {\left (2 \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^3-144 x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+72 e^{2 c_1} x \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+432 e^{2 c_1} x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \sin ^2(\alpha )+216 e^{2 c_1} x^2 \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ){}^2\right ){}^2-4 \left (24 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) x^2+24 e^{2 c_1} \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) x+\left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^2\right ){}^3}}}{6 \sqrt [3]{2}}+\frac {128 x^4-256 e^{c_1} \cos (\alpha ) x^3-96 e^{2 c_1} x^2+96 e^{2 c_1} \cos (2 \alpha ) x^2+48 e^{3 c_1} \cos (\alpha ) x-16 e^{3 c_1} \cos (3 \alpha ) x+3 e^{4 c_1}+4 e^{4 c_1} \cos (2 \alpha )+e^{4 c_1} \cos (4 \alpha )}{6\ 2^{2/3} \sqrt [3]{2 \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^3-144 x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+72 e^{2 c_1} x \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+432 e^{2 c_1} x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \sin ^2(\alpha )+216 e^{2 c_1} x^2 \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ){}^2+\sqrt {\left (2 \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^3-144 x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+72 e^{2 c_1} x \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+432 e^{2 c_1} x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \sin ^2(\alpha )+216 e^{2 c_1} x^2 \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ){}^2\right ){}^2-4 \left (24 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) x^2+24 e^{2 c_1} \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) x+\left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^2\right ){}^3}}}}}}\right \},\left \{y(x)\to -\frac {1}{2} e^{c_1} \sin (\alpha )-\frac {1}{2} \sqrt {e^{2 c_1} \sin ^2(\alpha )+\frac {1}{6} \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+\frac {1}{2} \left (-4 x^2+4 e^{c_1} \cos (\alpha ) x+e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right )+\frac {\sqrt [3]{2 \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^3-144 x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+72 e^{2 c_1} x \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+432 e^{2 c_1} x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \sin ^2(\alpha )+216 e^{2 c_1} x^2 \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ){}^2+\sqrt {\left (2 \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^3-144 x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+72 e^{2 c_1} x \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+432 e^{2 c_1} x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \sin ^2(\alpha )+216 e^{2 c_1} x^2 \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ){}^2\right ){}^2-4 \left (24 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) x^2+24 e^{2 c_1} \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) x+\left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^2\right ){}^3}}}{6 \sqrt [3]{2}}+\frac {128 x^4-256 e^{c_1} \cos (\alpha ) x^3-96 e^{2 c_1} x^2+96 e^{2 c_1} \cos (2 \alpha ) x^2+48 e^{3 c_1} \cos (\alpha ) x-16 e^{3 c_1} \cos (3 \alpha ) x+3 e^{4 c_1}+4 e^{4 c_1} \cos (2 \alpha )+e^{4 c_1} \cos (4 \alpha )}{6\ 2^{2/3} \sqrt [3]{2 \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^3-144 x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+72 e^{2 c_1} x \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+432 e^{2 c_1} x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \sin ^2(\alpha )+216 e^{2 c_1} x^2 \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ){}^2+\sqrt {\left (2 \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^3-144 x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+72 e^{2 c_1} x \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+432 e^{2 c_1} x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \sin ^2(\alpha )+216 e^{2 c_1} x^2 \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ){}^2\right ){}^2-4 \left (24 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) x^2+24 e^{2 c_1} \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) x+\left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^2\right ){}^3}}}}+\frac {1}{2} \sqrt {2 e^{2 c_1} \sin ^2(\alpha )+\frac {2}{3} \left (-4 x^2+4 e^{c_1} \cos (\alpha ) x+e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right )-\frac {\sqrt [3]{2 \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^3-144 x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+72 e^{2 c_1} x \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+432 e^{2 c_1} x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \sin ^2(\alpha )+216 e^{2 c_1} x^2 \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ){}^2+\sqrt {\left (2 \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^3-144 x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+72 e^{2 c_1} x \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+432 e^{2 c_1} x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \sin ^2(\alpha )+216 e^{2 c_1} x^2 \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ){}^2\right ){}^2-4 \left (24 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) x^2+24 e^{2 c_1} \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) x+\left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^2\right ){}^3}}}{6 \sqrt [3]{2}}-\frac {128 x^4-256 e^{c_1} \cos (\alpha ) x^3-96 e^{2 c_1} x^2+96 e^{2 c_1} \cos (2 \alpha ) x^2+48 e^{3 c_1} \cos (\alpha ) x-16 e^{3 c_1} \cos (3 \alpha ) x+3 e^{4 c_1}+4 e^{4 c_1} \cos (2 \alpha )+e^{4 c_1} \cos (4 \alpha )}{6\ 2^{2/3} \sqrt [3]{2 \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^3-144 x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+72 e^{2 c_1} x \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+432 e^{2 c_1} x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \sin ^2(\alpha )+216 e^{2 c_1} x^2 \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ){}^2+\sqrt {\left (2 \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^3-144 x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+72 e^{2 c_1} x \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+432 e^{2 c_1} x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \sin ^2(\alpha )+216 e^{2 c_1} x^2 \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ){}^2\right ){}^2-4 \left (24 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) x^2+24 e^{2 c_1} \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) x+\left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^2\right ){}^3}}}-\frac {-8 e^{3 c_1} \sin ^3(\alpha )+4 e^{c_1} \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ) \sin (\alpha )+8 e^{c_1} x \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right )}{4 \sqrt {e^{2 c_1} \sin ^2(\alpha )+\frac {1}{6} \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+\frac {1}{2} \left (-4 x^2+4 e^{c_1} \cos (\alpha ) x+e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right )+\frac {\sqrt [3]{2 \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^3-144 x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+72 e^{2 c_1} x \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+432 e^{2 c_1} x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \sin ^2(\alpha )+216 e^{2 c_1} x^2 \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ){}^2+\sqrt {\left (2 \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^3-144 x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+72 e^{2 c_1} x \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+432 e^{2 c_1} x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \sin ^2(\alpha )+216 e^{2 c_1} x^2 \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ){}^2\right ){}^2-4 \left (24 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) x^2+24 e^{2 c_1} \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) x+\left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^2\right ){}^3}}}{6 \sqrt [3]{2}}+\frac {128 x^4-256 e^{c_1} \cos (\alpha ) x^3-96 e^{2 c_1} x^2+96 e^{2 c_1} \cos (2 \alpha ) x^2+48 e^{3 c_1} \cos (\alpha ) x-16 e^{3 c_1} \cos (3 \alpha ) x+3 e^{4 c_1}+4 e^{4 c_1} \cos (2 \alpha )+e^{4 c_1} \cos (4 \alpha )}{6\ 2^{2/3} \sqrt [3]{2 \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^3-144 x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+72 e^{2 c_1} x \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+432 e^{2 c_1} x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \sin ^2(\alpha )+216 e^{2 c_1} x^2 \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ){}^2+\sqrt {\left (2 \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^3-144 x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+72 e^{2 c_1} x \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+432 e^{2 c_1} x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \sin ^2(\alpha )+216 e^{2 c_1} x^2 \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ){}^2\right ){}^2-4 \left (24 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) x^2+24 e^{2 c_1} \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) x+\left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^2\right ){}^3}}}}}}\right \},\left \{y(x)\to -\frac {1}{2} e^{c_1} \sin (\alpha )+\frac {1}{2} \sqrt {e^{2 c_1} \sin ^2(\alpha )+\frac {1}{6} \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+\frac {1}{2} \left (-4 x^2+4 e^{c_1} \cos (\alpha ) x+e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right )+\frac {\sqrt [3]{2 \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^3-144 x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+72 e^{2 c_1} x \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+432 e^{2 c_1} x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \sin ^2(\alpha )+216 e^{2 c_1} x^2 \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ){}^2+\sqrt {\left (2 \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^3-144 x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+72 e^{2 c_1} x \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+432 e^{2 c_1} x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \sin ^2(\alpha )+216 e^{2 c_1} x^2 \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ){}^2\right ){}^2-4 \left (24 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) x^2+24 e^{2 c_1} \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) x+\left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^2\right ){}^3}}}{6 \sqrt [3]{2}}+\frac {128 x^4-256 e^{c_1} \cos (\alpha ) x^3-96 e^{2 c_1} x^2+96 e^{2 c_1} \cos (2 \alpha ) x^2+48 e^{3 c_1} \cos (\alpha ) x-16 e^{3 c_1} \cos (3 \alpha ) x+3 e^{4 c_1}+4 e^{4 c_1} \cos (2 \alpha )+e^{4 c_1} \cos (4 \alpha )}{6\ 2^{2/3} \sqrt [3]{2 \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^3-144 x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+72 e^{2 c_1} x \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+432 e^{2 c_1} x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \sin ^2(\alpha )+216 e^{2 c_1} x^2 \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ){}^2+\sqrt {\left (2 \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^3-144 x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+72 e^{2 c_1} x \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+432 e^{2 c_1} x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \sin ^2(\alpha )+216 e^{2 c_1} x^2 \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ){}^2\right ){}^2-4 \left (24 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) x^2+24 e^{2 c_1} \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) x+\left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^2\right ){}^3}}}}-\frac {1}{2} \sqrt {2 e^{2 c_1} \sin ^2(\alpha )+\frac {2}{3} \left (-4 x^2+4 e^{c_1} \cos (\alpha ) x+e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right )-\frac {\sqrt [3]{2 \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^3-144 x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+72 e^{2 c_1} x \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+432 e^{2 c_1} x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \sin ^2(\alpha )+216 e^{2 c_1} x^2 \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ){}^2+\sqrt {\left (2 \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^3-144 x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+72 e^{2 c_1} x \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+432 e^{2 c_1} x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \sin ^2(\alpha )+216 e^{2 c_1} x^2 \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ){}^2\right ){}^2-4 \left (24 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) x^2+24 e^{2 c_1} \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) x+\left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^2\right ){}^3}}}{6 \sqrt [3]{2}}-\frac {128 x^4-256 e^{c_1} \cos (\alpha ) x^3-96 e^{2 c_1} x^2+96 e^{2 c_1} \cos (2 \alpha ) x^2+48 e^{3 c_1} \cos (\alpha ) x-16 e^{3 c_1} \cos (3 \alpha ) x+3 e^{4 c_1}+4 e^{4 c_1} \cos (2 \alpha )+e^{4 c_1} \cos (4 \alpha )}{6\ 2^{2/3} \sqrt [3]{2 \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^3-144 x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+72 e^{2 c_1} x \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+432 e^{2 c_1} x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \sin ^2(\alpha )+216 e^{2 c_1} x^2 \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ){}^2+\sqrt {\left (2 \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^3-144 x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+72 e^{2 c_1} x \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+432 e^{2 c_1} x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \sin ^2(\alpha )+216 e^{2 c_1} x^2 \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ){}^2\right ){}^2-4 \left (24 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) x^2+24 e^{2 c_1} \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) x+\left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^2\right ){}^3}}}+\frac {-8 e^{3 c_1} \sin ^3(\alpha )+4 e^{c_1} \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ) \sin (\alpha )+8 e^{c_1} x \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right )}{4 \sqrt {e^{2 c_1} \sin ^2(\alpha )+\frac {1}{6} \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+\frac {1}{2} \left (-4 x^2+4 e^{c_1} \cos (\alpha ) x+e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right )+\frac {\sqrt [3]{2 \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^3-144 x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+72 e^{2 c_1} x \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+432 e^{2 c_1} x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \sin ^2(\alpha )+216 e^{2 c_1} x^2 \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ){}^2+\sqrt {\left (2 \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^3-144 x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+72 e^{2 c_1} x \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+432 e^{2 c_1} x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \sin ^2(\alpha )+216 e^{2 c_1} x^2 \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ){}^2\right ){}^2-4 \left (24 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) x^2+24 e^{2 c_1} \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) x+\left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^2\right ){}^3}}}{6 \sqrt [3]{2}}+\frac {128 x^4-256 e^{c_1} \cos (\alpha ) x^3-96 e^{2 c_1} x^2+96 e^{2 c_1} \cos (2 \alpha ) x^2+48 e^{3 c_1} \cos (\alpha ) x-16 e^{3 c_1} \cos (3 \alpha ) x+3 e^{4 c_1}+4 e^{4 c_1} \cos (2 \alpha )+e^{4 c_1} \cos (4 \alpha )}{6\ 2^{2/3} \sqrt [3]{2 \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^3-144 x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+72 e^{2 c_1} x \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+432 e^{2 c_1} x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \sin ^2(\alpha )+216 e^{2 c_1} x^2 \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ){}^2+\sqrt {\left (2 \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^3-144 x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+72 e^{2 c_1} x \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+432 e^{2 c_1} x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \sin ^2(\alpha )+216 e^{2 c_1} x^2 \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ){}^2\right ){}^2-4 \left (24 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) x^2+24 e^{2 c_1} \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) x+\left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^2\right ){}^3}}}}}}\right \},\left \{y(x)\to -\frac {1}{2} e^{c_1} \sin (\alpha )+\frac {1}{2} \sqrt {e^{2 c_1} \sin ^2(\alpha )+\frac {1}{6} \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+\frac {1}{2} \left (-4 x^2+4 e^{c_1} \cos (\alpha ) x+e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right )+\frac {\sqrt [3]{2 \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^3-144 x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+72 e^{2 c_1} x \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+432 e^{2 c_1} x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \sin ^2(\alpha )+216 e^{2 c_1} x^2 \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ){}^2+\sqrt {\left (2 \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^3-144 x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+72 e^{2 c_1} x \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+432 e^{2 c_1} x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \sin ^2(\alpha )+216 e^{2 c_1} x^2 \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ){}^2\right ){}^2-4 \left (24 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) x^2+24 e^{2 c_1} \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) x+\left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^2\right ){}^3}}}{6 \sqrt [3]{2}}+\frac {128 x^4-256 e^{c_1} \cos (\alpha ) x^3-96 e^{2 c_1} x^2+96 e^{2 c_1} \cos (2 \alpha ) x^2+48 e^{3 c_1} \cos (\alpha ) x-16 e^{3 c_1} \cos (3 \alpha ) x+3 e^{4 c_1}+4 e^{4 c_1} \cos (2 \alpha )+e^{4 c_1} \cos (4 \alpha )}{6\ 2^{2/3} \sqrt [3]{2 \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^3-144 x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+72 e^{2 c_1} x \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+432 e^{2 c_1} x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \sin ^2(\alpha )+216 e^{2 c_1} x^2 \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ){}^2+\sqrt {\left (2 \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^3-144 x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+72 e^{2 c_1} x \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+432 e^{2 c_1} x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \sin ^2(\alpha )+216 e^{2 c_1} x^2 \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ){}^2\right ){}^2-4 \left (24 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) x^2+24 e^{2 c_1} \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) x+\left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^2\right ){}^3}}}}+\frac {1}{2} \sqrt {2 e^{2 c_1} \sin ^2(\alpha )+\frac {2}{3} \left (-4 x^2+4 e^{c_1} \cos (\alpha ) x+e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right )-\frac {\sqrt [3]{2 \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^3-144 x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+72 e^{2 c_1} x \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+432 e^{2 c_1} x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \sin ^2(\alpha )+216 e^{2 c_1} x^2 \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ){}^2+\sqrt {\left (2 \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^3-144 x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+72 e^{2 c_1} x \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+432 e^{2 c_1} x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \sin ^2(\alpha )+216 e^{2 c_1} x^2 \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ){}^2\right ){}^2-4 \left (24 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) x^2+24 e^{2 c_1} \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) x+\left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^2\right ){}^3}}}{6 \sqrt [3]{2}}-\frac {128 x^4-256 e^{c_1} \cos (\alpha ) x^3-96 e^{2 c_1} x^2+96 e^{2 c_1} \cos (2 \alpha ) x^2+48 e^{3 c_1} \cos (\alpha ) x-16 e^{3 c_1} \cos (3 \alpha ) x+3 e^{4 c_1}+4 e^{4 c_1} \cos (2 \alpha )+e^{4 c_1} \cos (4 \alpha )}{6\ 2^{2/3} \sqrt [3]{2 \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^3-144 x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+72 e^{2 c_1} x \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+432 e^{2 c_1} x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \sin ^2(\alpha )+216 e^{2 c_1} x^2 \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ){}^2+\sqrt {\left (2 \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^3-144 x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+72 e^{2 c_1} x \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+432 e^{2 c_1} x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \sin ^2(\alpha )+216 e^{2 c_1} x^2 \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ){}^2\right ){}^2-4 \left (24 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) x^2+24 e^{2 c_1} \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) x+\left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^2\right ){}^3}}}+\frac {-8 e^{3 c_1} \sin ^3(\alpha )+4 e^{c_1} \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ) \sin (\alpha )+8 e^{c_1} x \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right )}{4 \sqrt {e^{2 c_1} \sin ^2(\alpha )+\frac {1}{6} \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+\frac {1}{2} \left (-4 x^2+4 e^{c_1} \cos (\alpha ) x+e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right )+\frac {\sqrt [3]{2 \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^3-144 x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+72 e^{2 c_1} x \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+432 e^{2 c_1} x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \sin ^2(\alpha )+216 e^{2 c_1} x^2 \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ){}^2+\sqrt {\left (2 \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^3-144 x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+72 e^{2 c_1} x \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+432 e^{2 c_1} x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \sin ^2(\alpha )+216 e^{2 c_1} x^2 \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ){}^2\right ){}^2-4 \left (24 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) x^2+24 e^{2 c_1} \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) x+\left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^2\right ){}^3}}}{6 \sqrt [3]{2}}+\frac {128 x^4-256 e^{c_1} \cos (\alpha ) x^3-96 e^{2 c_1} x^2+96 e^{2 c_1} \cos (2 \alpha ) x^2+48 e^{3 c_1} \cos (\alpha ) x-16 e^{3 c_1} \cos (3 \alpha ) x+3 e^{4 c_1}+4 e^{4 c_1} \cos (2 \alpha )+e^{4 c_1} \cos (4 \alpha )}{6\ 2^{2/3} \sqrt [3]{2 \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^3-144 x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+72 e^{2 c_1} x \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+432 e^{2 c_1} x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \sin ^2(\alpha )+216 e^{2 c_1} x^2 \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ){}^2+\sqrt {\left (2 \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^3-144 x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+72 e^{2 c_1} x \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) \left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right )+432 e^{2 c_1} x^2 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) \sin ^2(\alpha )+216 e^{2 c_1} x^2 \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ){}^2\right ){}^2-4 \left (24 \left (2 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}+e^{2 c_1} \cos (2 \alpha )\right ) x^2+24 e^{2 c_1} \sin (\alpha ) \left (e^{c_1} \sin (2 \alpha )-2 x \sin (\alpha )\right ) x+\left (4 x^2-4 e^{c_1} \cos (\alpha ) x-e^{2 c_1}-e^{2 c_1} \cos (2 \alpha )\right ){}^2\right ){}^3}}}}}}\right \}\right \} \]
Maple: cpu = 0.530 (sec), leaf count = 136 \[ \left \{ y \left ( x \right ) ={\it RootOf} \left ( -\ln \left ( x \right ) +\int ^{{\it \_Z}}\!-{\frac {1}{ \left ( {{\it \_a}}^{2}+1 \right ) \left ( \cos \left ( 2\,\alpha \right ) {{\it \_a}}^{2}+2\,{ \it \_a}\,\sin \left ( 2\,\alpha \right ) +{{\it \_a}}^{2}-\cos \left ( 2 \,\alpha \right ) +1 \right ) } \left ( \cos \left ( 2\,\alpha \right ) {{ \it \_a}}^{3}+3\,\sin \left ( 2\,\alpha \right ) {{\it \_a}}^{2}+{{\it \_a}}^{3}-3\,\cos \left ( 2\,\alpha \right ) {\it \_a}-\sin \left ( 2\, \alpha \right ) -\sqrt {2\,\cos \left ( 2\,\alpha \right ) {{\it \_a}}^{4 }+4\,\sin \left ( 2\,\alpha \right ) {{\it \_a}}^{3}+2\,{{\it \_a}}^{4}+ 4\,{\it \_a}\,\sin \left ( 2\,\alpha \right ) +4\,{{\it \_a}}^{2}-2\, \cos \left ( 2\,\alpha \right ) +2}+{\it \_a} \right ) }{d{\it \_a}}+{ \it \_C1} \right ) x \right \} \]