\[ y'(x) \left (\sin (\alpha ) \left (y(x)^2-x^2\right )-2 x \cos (\alpha ) y(x)+\sqrt {x^2+y(x)^2} y(x)\right )+\cos (\alpha ) \left (y(x)^2-x^2\right )+2 x \sin (\alpha ) y(x)+x \sqrt {x^2+y(x)^2}=0 \] ✓ Mathematica : cpu = 102.971 (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 = 0.744 (sec), leaf count = 129
\[ \left \{ y \left ( x \right ) ={\it RootOf} \left ( -\ln \left ( x \right ) +\int ^{{\it \_Z}}\!{\frac {1}{ \left ( {{\it \_a}}^{2}+1 \right ) \left ( \cos \left ( 2\,\alpha \right ) {{\it \_a}}^{2}+2\,{\it \_a}\,\sin \left ( 2\,\alpha \right ) +{{\it \_a}}^{2}-\cos \left ( 2\,\alpha \right ) +1 \right ) } \left ( -\cos \left ( 2\,\alpha \right ) {{\it \_a}}^{3}-3\,\sin \left ( 2\,\alpha \right ) {{\it \_a}}^{2}-{{\it \_a}}^{3}+\sqrt {2}\sqrt { \left ( {{\it \_a}}^{2}+1 \right ) \left ( \cos \left ( 2\,\alpha \right ) {{\it \_a}}^{2}+2\,{\it \_a}\,\sin \left ( 2\,\alpha \right ) +{{\it \_a}}^{2}-\cos \left ( 2\,\alpha \right ) +1 \right ) }+3\,\cos \left ( 2\,\alpha \right ) {\it \_a}+\sin \left ( 2\,\alpha \right ) -{\it \_a} \right ) }{d{\it \_a}}+{\it \_C1} \right ) x \right \} \]