2.430   ODE No. 430

  1. Problem in Latex
  2. Mathematica input
  3. Maple input

\[ \text {a0} x+y'(x) (\text {a1} x+\text {b1} y(x)+\text {c1})+(\text {a2} x+\text {c2}) y'(x)^2+\text {b0} y(x)+\text {c0}=0 \] Mathematica : cpu = 258.223 (sec), leaf count = 478

\[\text {Solve}\left [\left \{x=c_1 (\text {b0}+\text {b1} \text {K$\$$38189}) \exp \left (\frac {(\text {b1} (\text {b0}-\text {a1})+2 \text {a2} \text {b0}) \tan ^{-1}\left (\frac {\text {a1}+2 \text {K$\$$38189} (\text {a2}+\text {b1})+\text {b0}}{\sqrt {4 \text {a0} (\text {a2}+\text {b1})-\text {a1}^2-2 \text {a1} \text {b0}-\text {b0}^2}}\right )}{(\text {a2}+\text {b1}) \sqrt {4 \text {a0} (\text {a2}+\text {b1})-\text {a1}^2-2 \text {a1} \text {b0}-\text {b0}^2}}-\frac {(2 \text {a2}+\text {b1}) \log (\text {a0}+\text {K$\$$38189} (\text {a1}+\text {K$\$$38189} (\text {a2}+\text {b1})+\text {b0}))}{2 (\text {a2}+\text {b1})}\right )+(\text {b0}+\text {b1} \text {K$\$$38189}) \exp \left (\frac {(\text {b1} (\text {b0}-\text {a1})+2 \text {a2} \text {b0}) \tan ^{-1}\left (\frac {\text {a1}+2 \text {K$\$$38189} (\text {a2}+\text {b1})+\text {b0}}{\sqrt {4 \text {a0} (\text {a2}+\text {b1})-\text {a1}^2-2 \text {a1} \text {b0}-\text {b0}^2}}\right )}{(\text {a2}+\text {b1}) \sqrt {4 \text {a0} (\text {a2}+\text {b1})-\text {a1}^2-2 \text {a1} \text {b0}-\text {b0}^2}}-\frac {(2 \text {a2}+\text {b1}) \log (\text {a0}+\text {K$\$$38189} (\text {a1}+\text {K$\$$38189} (\text {a2}+\text {b1})+\text {b0}))}{2 (\text {a2}+\text {b1})}\right ) \int \frac {\left (\frac {-\text {c1}-2 \text {c2} \text {K$\$$38189}}{\text {b0}+\text {b1} \text {K$\$$38189}}-\frac {\text {b1} \left (-\text {c0}-\text {c1} \text {K$\$$38189}-\text {c2} \text {K$\$$38189}^2\right )}{(\text {b0}+\text {b1} \text {K$\$$38189})^2}\right ) \exp \left (\frac {(2 \text {a2}+\text {b1}) \log (\text {a0}+\text {K$\$$38189} (\text {a1}+\text {K$\$$38189} (\text {a2}+\text {b1})+\text {b0}))}{2 (\text {a2}+\text {b1})}-\frac {(\text {b1} (\text {b0}-\text {a1})+2 \text {a2} \text {b0}) \tan ^{-1}\left (\frac {\text {a1}+2 \text {K$\$$38189} (\text {a2}+\text {b1})+\text {b0}}{\sqrt {4 \text {a0} (\text {a2}+\text {b1})-\text {a1}^2-2 \text {a1} \text {b0}-\text {b0}^2}}\right )}{(\text {a2}+\text {b1}) \sqrt {4 \text {a0} (\text {a2}+\text {b1})-\text {a1}^2-2 \text {a1} \text {b0}-\text {b0}^2}}\right )}{(\text {b0}+\text {b1} \text {K$\$$38189}) \left (\text {K$\$$38189}-\frac {-\text {a0}-\text {a1} \text {K$\$$38189}-\text {a2} \text {K$\$$38189}^2}{\text {b0}+\text {b1} \text {K$\$$38189}}\right )} \, d\text {K$\$$38189},y(x)=\frac {x \left (-\text {a0}-\text {a1} \text {K$\$$38189}-\text {a2} \text {K$\$$38189}^2\right )}{\text {b0}+\text {b1} \text {K$\$$38189}}+\frac {-\text {c0}-\text {c1} \text {K$\$$38189}-\text {c2} \text {K$\$$38189}^2}{\text {b0}+\text {b1} \text {K$\$$38189}}\right \},\{y(x),\text {K$\$$38189}\}\right ]\]

Maple : cpu = 1.089 (sec), leaf count = 9885

\[ \left \{ {\frac {{\it \_C1}}{{\it a2}\,x+{\it c2}} \left ( {\it a1}\,{\it b1}\,x-2\,{\it a2}\,{\it b0}\,x+{{\it b1}}^{2}y \left ( x \right ) +\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it b1}-2\,{\it b0}\,{\it c2}+{\it b1}\,{\it c1} \right ) \left ( {\frac {1}{2\, \left ( {\it a2}\,x+{\it c2} \right ) ^{2}} \left ( {\it a1}\,{\it a2}\,{\it c1}\,x+2\,{\it a1}\,{\it b1}\,{\it c1}\,x-{\it a1}\,{\it a2}\,{\it b0}\,{x}^{2}-{\it a1}\,{\it b0}\,{\it c2}\,x-{\it a2}\,{\it b0}\,{\it c1}\,x+2\,{\it a0}\,{\it a2}\,{\it c2}\,x-2\,{\it a0}\,{\it a2}\,{\it b1}\,{x}^{2}+{{\it b1}}^{3} \left ( y \left ( x \right ) \right ) ^{2}+{\it a2}\,{{\it c1}}^{2}+{\it b1}\,{{\it c1}}^{2}+2\,{\it a0}\,{{\it c2}}^{2}+2\,{\it a2}\,{\it b1}\,{\it c1}\,y \left ( x \right ) +2\,{\it a1}\,{{\it b1}}^{2}xy \left ( x \right ) -{\it a1}\,{\it b1}\,{\it c2}\,y \left ( x \right ) -3\,{\it b0}\,{\it b1}\,{\it c2}\,y \left ( x \right ) +\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it a1}\,{\it b1}\,x-\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it a2}\,{\it b0}\,x+\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it a2}\,{\it b1}\,y \left ( x \right ) -2\,{{\it a2}}^{2}{\it b0}\,xy \left ( x \right ) -2\,{\it a2}\,{\it b0}\,{\it c2}\,y \left ( x \right ) -2\,{\it a0}\,{\it b1}\,{\it c2}\,x-2\,{\it a2}\,{\it b1}\,{\it c0}\,x+2\,{{\it b1}}^{2}{\it c1}\,y \left ( x \right ) +\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{{\it b1}}^{2}y \left ( x \right ) -\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it a1}\,{\it c2}+\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it a2}\,{\it c1}-\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it b0}\,{\it c2}+\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it b1}\,{\it c1}+{\it a2}\,{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-{{\it a1}}^{2}{\it c2}\,x-{\it a1}\,{\it c1}\,{\it c2}-{\it b0}\,{\it c1}\,{\it c2}-2\,{{\it a2}}^{2}{\it c0}\,x-2\,{\it a2}\,{\it c0}\,{\it c2}-2\,{\it b1}\,{\it c0}\,{\it c2}+{{\it a1}}^{2}{\it b1}\,{x}^{2}+{\it a1}\,{\it a2}\,{\it b1}\,xy \left ( x \right ) -3\,{\it a2}\,{\it b0}\,{\it b1}\,xy \left ( x \right ) \right ) } \right ) ^{-{\frac {2\,{\it a2}+{\it b1}}{2\,{\it a2}+2\,{\it b1}}}}{{\rm e}^{-2\,{\frac {{\it a1}\,{\it a2}}{\sqrt {4\,{\it a0}\,{\it a2}+4\,{\it a0}\,{\it b1}-{{\it a1}}^{2}-2\,{\it a1}\,{\it b0}-{{\it b0}}^{2}} \left ( {\it a2}+{\it b1} \right ) }\arctan \left ( {\frac {{\it a1}\,{\it b1}\,x-{\it a2}\,{\it b0}\,x+{\it a2}\,{\it b1}\,y \left ( x \right ) +{{\it b1}}^{2}y \left ( x \right ) +\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it a2}+\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it b1}-{\it a1}\,{\it c2}+{\it a2}\,{\it c1}-{\it b0}\,{\it c2}+{\it b1}\,{\it c1}}{ \left ( {\it a2}\,x+{\it c2} \right ) \sqrt {4\,{\it a0}\,{\it a2}+4\,{\it a0}\,{\it b1}-{{\it a1}}^{2}-2\,{\it a1}\,{\it b0}-{{\it b0}}^{2}}}} \right ) }-{\frac {{\it b1}\,{\it a1}}{{\it a2}+{\it b1}}\arctan \left ( {\frac {1}{{\it a2}\,x+{\it c2}} \left ( {\it a1}\,{\it b1}\,x-{\it a2}\,{\it b0}\,x+{\it a2}\,{\it b1}\,y \left ( x \right ) +{{\it b1}}^{2}y \left ( x \right ) +\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it a2}+\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it b1}-{\it a1}\,{\it c2}+{\it a2}\,{\it c1}-{\it b0}\,{\it c2}+{\it b1}\,{\it c1} \right ) {\frac {1}{\sqrt {4\,{\it a0}\,{\it a2}+4\,{\it a0}\,{\it b1}-{{\it a1}}^{2}-2\,{\it a1}\,{\it b0}-{{\it b0}}^{2}}}}} \right ) {\frac {1}{\sqrt {4\,{\it a0}\,{\it a2}+4\,{\it a0}\,{\it b1}-{{\it a1}}^{2}-2\,{\it a1}\,{\it b0}-{{\it b0}}^{2}}}}}-2\,{\frac {{\it b0}\,{\it a2}}{\sqrt {4\,{\it a0}\,{\it a2}+4\,{\it a0}\,{\it b1}-{{\it a1}}^{2}-2\,{\it a1}\,{\it b0}-{{\it b0}}^{2}} \left ( {\it a2}+{\it b1} \right ) }\arctan \left ( {\frac {{\it a1}\,{\it b1}\,x-{\it a2}\,{\it b0}\,x+{\it a2}\,{\it b1}\,y \left ( x \right ) +{{\it b1}}^{2}y \left ( x \right ) +\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it a2}+\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it b1}-{\it a1}\,{\it c2}+{\it a2}\,{\it c1}-{\it b0}\,{\it c2}+{\it b1}\,{\it c1}}{ \left ( {\it a2}\,x+{\it c2} \right ) \sqrt {4\,{\it a0}\,{\it a2}+4\,{\it a0}\,{\it b1}-{{\it a1}}^{2}-2\,{\it a1}\,{\it b0}-{{\it b0}}^{2}}}} \right ) }-{\frac {{\it b1}\,{\it b0}}{{\it a2}+{\it b1}}\arctan \left ( {\frac {1}{{\it a2}\,x+{\it c2}} \left ( {\it a1}\,{\it b1}\,x-{\it a2}\,{\it b0}\,x+{\it a2}\,{\it b1}\,y \left ( x \right ) +{{\it b1}}^{2}y \left ( x \right ) +\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it a2}+\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it b1}-{\it a1}\,{\it c2}+{\it a2}\,{\it c1}-{\it b0}\,{\it c2}+{\it b1}\,{\it c1} \right ) {\frac {1}{\sqrt {4\,{\it a0}\,{\it a2}+4\,{\it a0}\,{\it b1}-{{\it a1}}^{2}-2\,{\it a1}\,{\it b0}-{{\it b0}}^{2}}}}} \right ) {\frac {1}{\sqrt {4\,{\it a0}\,{\it a2}+4\,{\it a0}\,{\it b1}-{{\it a1}}^{2}-2\,{\it a1}\,{\it b0}-{{\it b0}}^{2}}}}}+2\,{\frac {{\it a1}}{\sqrt {4\,{\it a0}\,{\it a2}+4\,{\it a0}\,{\it b1}-{{\it a1}}^{2}-2\,{\it a1}\,{\it b0}-{{\it b0}}^{2}}}\arctan \left ( {\frac {{\it a1}\,{\it b1}\,x-{\it a2}\,{\it b0}\,x+{\it a2}\,{\it b1}\,y \left ( x \right ) +{{\it b1}}^{2}y \left ( x \right ) +\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it a2}+\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it b1}-{\it a1}\,{\it c2}+{\it a2}\,{\it c1}-{\it b0}\,{\it c2}+{\it b1}\,{\it c1}}{ \left ( {\it a2}\,x+{\it c2} \right ) \sqrt {4\,{\it a0}\,{\it a2}+4\,{\it a0}\,{\it b1}-{{\it a1}}^{2}-2\,{\it a1}\,{\it b0}-{{\it b0}}^{2}}}} \right ) }}}}+x+{\frac {1}{2\,{\it a2}\,x+2\,{\it c2}} \left ( {\it a1}\,{\it b1}\,x-2\,{\it a2}\,{\it b0}\,x+{{\it b1}}^{2}y \left ( x \right ) +\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it b1}-2\,{\it b0}\,{\it c2}+{\it b1}\,{\it c1} \right ) \int ^{-{\frac {1}{2\,{\it a2}\,x+2\,{\it c2}} \left ( {\it a1}\,x+{\it b1}\,y \left ( x \right ) +\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}+{\it c1} \right ) }}\!-{\frac {{{\it \_a}}^{2}{\it b1}\,{\it c2}+2\,{\it \_a}\,{\it b0}\,{\it c2}+{\it b0}\,{\it c1}-{\it b1}\,{\it c0}}{ \left ( {\it \_a}\,{\it b1}+{\it b0} \right ) ^{2}} \left ( {{\it \_a}}^{2}{\it a2}+{{\it \_a}}^{2}{\it b1}+{\it \_a}\,{\it a1}+{\it \_a}\,{\it b0}+{\it a0} \right ) ^{-{\frac {{\it b1}}{2\,{\it a2}+2\,{\it b1}}}}{{\rm e}^{2\,{\frac {{\it a1}}{\sqrt {4\,{\it a0}\,{\it a2}+4\,{\it a0}\,{\it b1}-{{\it a1}}^{2}-2\,{\it a1}\,{\it b0}-{{\it b0}}^{2}}}\arctan \left ( {\frac {2\,{\it \_a}\,{\it a2}+2\,{\it \_a}\,{\it b1}+{\it a1}+{\it b0}}{\sqrt {4\,{\it a0}\,{\it a2}+4\,{\it a0}\,{\it b1}-{{\it a1}}^{2}-2\,{\it a1}\,{\it b0}-{{\it b0}}^{2}}}} \right ) }-{\frac {{\it b1}\,{\it b0}}{{\it a2}+{\it b1}}\arctan \left ( {(2\,{\it \_a}\,{\it a2}+2\,{\it \_a}\,{\it b1}+{\it a1}+{\it b0}){\frac {1}{\sqrt {4\,{\it a0}\,{\it a2}+4\,{\it a0}\,{\it b1}-{{\it a1}}^{2}-2\,{\it a1}\,{\it b0}-{{\it b0}}^{2}}}}} \right ) {\frac {1}{\sqrt {4\,{\it a0}\,{\it a2}+4\,{\it a0}\,{\it b1}-{{\it a1}}^{2}-2\,{\it a1}\,{\it b0}-{{\it b0}}^{2}}}}}-2\,{\frac {{\it b0}\,{\it a2}}{\sqrt {4\,{\it a0}\,{\it a2}+4\,{\it a0}\,{\it b1}-{{\it a1}}^{2}-2\,{\it a1}\,{\it b0}-{{\it b0}}^{2}} \left ( {\it a2}+{\it b1} \right ) }\arctan \left ( {\frac {2\,{\it \_a}\,{\it a2}+2\,{\it \_a}\,{\it b1}+{\it a1}+{\it b0}}{\sqrt {4\,{\it a0}\,{\it a2}+4\,{\it a0}\,{\it b1}-{{\it a1}}^{2}-2\,{\it a1}\,{\it b0}-{{\it b0}}^{2}}}} \right ) }-{\frac {{\it b1}\,{\it a1}}{{\it a2}+{\it b1}}\arctan \left ( {(2\,{\it \_a}\,{\it a2}+2\,{\it \_a}\,{\it b1}+{\it a1}+{\it b0}){\frac {1}{\sqrt {4\,{\it a0}\,{\it a2}+4\,{\it a0}\,{\it b1}-{{\it a1}}^{2}-2\,{\it a1}\,{\it b0}-{{\it b0}}^{2}}}}} \right ) {\frac {1}{\sqrt {4\,{\it a0}\,{\it a2}+4\,{\it a0}\,{\it b1}-{{\it a1}}^{2}-2\,{\it a1}\,{\it b0}-{{\it b0}}^{2}}}}}-2\,{\frac {{\it a1}\,{\it a2}}{\sqrt {4\,{\it a0}\,{\it a2}+4\,{\it a0}\,{\it b1}-{{\it a1}}^{2}-2\,{\it a1}\,{\it b0}-{{\it b0}}^{2}} \left ( {\it a2}+{\it b1} \right ) }\arctan \left ( {\frac {2\,{\it \_a}\,{\it a2}+2\,{\it \_a}\,{\it b1}+{\it a1}+{\it b0}}{\sqrt {4\,{\it a0}\,{\it a2}+4\,{\it a0}\,{\it b1}-{{\it a1}}^{2}-2\,{\it a1}\,{\it b0}-{{\it b0}}^{2}}}} \right ) }}}}{d{\it \_a}} \left ( {\frac {1}{2\, \left ( {\it a2}\,x+{\it c2} \right ) ^{2}} \left ( {\it a1}\,{\it a2}\,{\it c1}\,x+2\,{\it a1}\,{\it b1}\,{\it c1}\,x-{\it a1}\,{\it a2}\,{\it b0}\,{x}^{2}-{\it a1}\,{\it b0}\,{\it c2}\,x-{\it a2}\,{\it b0}\,{\it c1}\,x+2\,{\it a0}\,{\it a2}\,{\it c2}\,x-2\,{\it a0}\,{\it a2}\,{\it b1}\,{x}^{2}+{{\it b1}}^{3} \left ( y \left ( x \right ) \right ) ^{2}+{\it a2}\,{{\it c1}}^{2}+{\it b1}\,{{\it c1}}^{2}+2\,{\it a0}\,{{\it c2}}^{2}+2\,{\it a2}\,{\it b1}\,{\it c1}\,y \left ( x \right ) +2\,{\it a1}\,{{\it b1}}^{2}xy \left ( x \right ) -{\it a1}\,{\it b1}\,{\it c2}\,y \left ( x \right ) -3\,{\it b0}\,{\it b1}\,{\it c2}\,y \left ( x \right ) +\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it a1}\,{\it b1}\,x-\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it a2}\,{\it b0}\,x+\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it a2}\,{\it b1}\,y \left ( x \right ) -2\,{{\it a2}}^{2}{\it b0}\,xy \left ( x \right ) -2\,{\it a2}\,{\it b0}\,{\it c2}\,y \left ( x \right ) -2\,{\it a0}\,{\it b1}\,{\it c2}\,x-2\,{\it a2}\,{\it b1}\,{\it c0}\,x+2\,{{\it b1}}^{2}{\it c1}\,y \left ( x \right ) +\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{{\it b1}}^{2}y \left ( x \right ) -\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it a1}\,{\it c2}+\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it a2}\,{\it c1}-\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it b0}\,{\it c2}+\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it b1}\,{\it c1}+{\it a2}\,{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-{{\it a1}}^{2}{\it c2}\,x-{\it a1}\,{\it c1}\,{\it c2}-{\it b0}\,{\it c1}\,{\it c2}-2\,{{\it a2}}^{2}{\it c0}\,x-2\,{\it a2}\,{\it c0}\,{\it c2}-2\,{\it b1}\,{\it c0}\,{\it c2}+{{\it a1}}^{2}{\it b1}\,{x}^{2}+{\it a1}\,{\it a2}\,{\it b1}\,xy \left ( x \right ) -3\,{\it a2}\,{\it b0}\,{\it b1}\,xy \left ( x \right ) \right ) } \right ) ^{-{\frac {2\,{\it a2}+{\it b1}}{2\,{\it a2}+2\,{\it b1}}}}{{\rm e}^{-2\,{\frac {{\it a1}\,{\it a2}}{\sqrt {4\,{\it a0}\,{\it a2}+4\,{\it a0}\,{\it b1}-{{\it a1}}^{2}-2\,{\it a1}\,{\it b0}-{{\it b0}}^{2}} \left ( {\it a2}+{\it b1} \right ) }\arctan \left ( {\frac {{\it a1}\,{\it b1}\,x-{\it a2}\,{\it b0}\,x+{\it a2}\,{\it b1}\,y \left ( x \right ) +{{\it b1}}^{2}y \left ( x \right ) +\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it a2}+\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it b1}-{\it a1}\,{\it c2}+{\it a2}\,{\it c1}-{\it b0}\,{\it c2}+{\it b1}\,{\it c1}}{ \left ( {\it a2}\,x+{\it c2} \right ) \sqrt {4\,{\it a0}\,{\it a2}+4\,{\it a0}\,{\it b1}-{{\it a1}}^{2}-2\,{\it a1}\,{\it b0}-{{\it b0}}^{2}}}} \right ) }-{\frac {{\it b1}\,{\it a1}}{{\it a2}+{\it b1}}\arctan \left ( {\frac {1}{{\it a2}\,x+{\it c2}} \left ( {\it a1}\,{\it b1}\,x-{\it a2}\,{\it b0}\,x+{\it a2}\,{\it b1}\,y \left ( x \right ) +{{\it b1}}^{2}y \left ( x \right ) +\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it a2}+\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it b1}-{\it a1}\,{\it c2}+{\it a2}\,{\it c1}-{\it b0}\,{\it c2}+{\it b1}\,{\it c1} \right ) {\frac {1}{\sqrt {4\,{\it a0}\,{\it a2}+4\,{\it a0}\,{\it b1}-{{\it a1}}^{2}-2\,{\it a1}\,{\it b0}-{{\it b0}}^{2}}}}} \right ) {\frac {1}{\sqrt {4\,{\it a0}\,{\it a2}+4\,{\it a0}\,{\it b1}-{{\it a1}}^{2}-2\,{\it a1}\,{\it b0}-{{\it b0}}^{2}}}}}-2\,{\frac {{\it b0}\,{\it a2}}{\sqrt {4\,{\it a0}\,{\it a2}+4\,{\it a0}\,{\it b1}-{{\it a1}}^{2}-2\,{\it a1}\,{\it b0}-{{\it b0}}^{2}} \left ( {\it a2}+{\it b1} \right ) }\arctan \left ( {\frac {{\it a1}\,{\it b1}\,x-{\it a2}\,{\it b0}\,x+{\it a2}\,{\it b1}\,y \left ( x \right ) +{{\it b1}}^{2}y \left ( x \right ) +\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it a2}+\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it b1}-{\it a1}\,{\it c2}+{\it a2}\,{\it c1}-{\it b0}\,{\it c2}+{\it b1}\,{\it c1}}{ \left ( {\it a2}\,x+{\it c2} \right ) \sqrt {4\,{\it a0}\,{\it a2}+4\,{\it a0}\,{\it b1}-{{\it a1}}^{2}-2\,{\it a1}\,{\it b0}-{{\it b0}}^{2}}}} \right ) }-{\frac {{\it b1}\,{\it b0}}{{\it a2}+{\it b1}}\arctan \left ( {\frac {1}{{\it a2}\,x+{\it c2}} \left ( {\it a1}\,{\it b1}\,x-{\it a2}\,{\it b0}\,x+{\it a2}\,{\it b1}\,y \left ( x \right ) +{{\it b1}}^{2}y \left ( x \right ) +\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it a2}+\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it b1}-{\it a1}\,{\it c2}+{\it a2}\,{\it c1}-{\it b0}\,{\it c2}+{\it b1}\,{\it c1} \right ) {\frac {1}{\sqrt {4\,{\it a0}\,{\it a2}+4\,{\it a0}\,{\it b1}-{{\it a1}}^{2}-2\,{\it a1}\,{\it b0}-{{\it b0}}^{2}}}}} \right ) {\frac {1}{\sqrt {4\,{\it a0}\,{\it a2}+4\,{\it a0}\,{\it b1}-{{\it a1}}^{2}-2\,{\it a1}\,{\it b0}-{{\it b0}}^{2}}}}}+2\,{\frac {{\it a1}}{\sqrt {4\,{\it a0}\,{\it a2}+4\,{\it a0}\,{\it b1}-{{\it a1}}^{2}-2\,{\it a1}\,{\it b0}-{{\it b0}}^{2}}}\arctan \left ( {\frac {{\it a1}\,{\it b1}\,x-{\it a2}\,{\it b0}\,x+{\it a2}\,{\it b1}\,y \left ( x \right ) +{{\it b1}}^{2}y \left ( x \right ) +\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it a2}+\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it b1}-{\it a1}\,{\it c2}+{\it a2}\,{\it c1}-{\it b0}\,{\it c2}+{\it b1}\,{\it c1}}{ \left ( {\it a2}\,x+{\it c2} \right ) \sqrt {4\,{\it a0}\,{\it a2}+4\,{\it a0}\,{\it b1}-{{\it a1}}^{2}-2\,{\it a1}\,{\it b0}-{{\it b0}}^{2}}}} \right ) }}}}=0,{\frac {{\it \_C1}}{{\it a2}\,x+{\it c2}} \left ( -{\it a1}\,{\it b1}\,x+2\,{\it a2}\,{\it b0}\,x-{{\it b1}}^{2}y \left ( x \right ) +\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it b1}+2\,{\it b0}\,{\it c2}-{\it b1}\,{\it c1} \right ) \left ( -{\frac {1}{2\, \left ( {\it a2}\,x+{\it c2} \right ) ^{2}} \left ( -{\it a1}\,{\it a2}\,{\it c1}\,x-2\,{\it a1}\,{\it b1}\,{\it c1}\,x+{\it a1}\,{\it a2}\,{\it b0}\,{x}^{2}+{\it a1}\,{\it b0}\,{\it c2}\,x+{\it a2}\,{\it b0}\,{\it c1}\,x-2\,{\it a0}\,{\it a2}\,{\it c2}\,x+2\,{\it a0}\,{\it a2}\,{\it b1}\,{x}^{2}-{{\it b1}}^{3} \left ( y \left ( x \right ) \right ) ^{2}-{\it a2}\,{{\it c1}}^{2}-{\it b1}\,{{\it c1}}^{2}-2\,{\it a0}\,{{\it c2}}^{2}-2\,{\it a2}\,{\it b1}\,{\it c1}\,y \left ( x \right ) -2\,{\it a1}\,{{\it b1}}^{2}xy \left ( x \right ) +{\it a1}\,{\it b1}\,{\it c2}\,y \left ( x \right ) +3\,{\it b0}\,{\it b1}\,{\it c2}\,y \left ( x \right ) +\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it a1}\,{\it b1}\,x-\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it a2}\,{\it b0}\,x+\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it a2}\,{\it b1}\,y \left ( x \right ) +2\,{{\it a2}}^{2}{\it b0}\,xy \left ( x \right ) +2\,{\it a2}\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it a0}\,{\it b1}\,{\it c2}\,x+2\,{\it a2}\,{\it b1}\,{\it c0}\,x-2\,{{\it b1}}^{2}{\it c1}\,y \left ( x \right ) +\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{{\it b1}}^{2}y \left ( x \right ) -\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it a1}\,{\it c2}+\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it a2}\,{\it c1}-\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it b0}\,{\it c2}+\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it b1}\,{\it c1}-{\it a2}\,{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}+{{\it a1}}^{2}{\it c2}\,x+{\it a1}\,{\it c1}\,{\it c2}+{\it b0}\,{\it c1}\,{\it c2}+2\,{{\it a2}}^{2}{\it c0}\,x+2\,{\it a2}\,{\it c0}\,{\it c2}+2\,{\it b1}\,{\it c0}\,{\it c2}-{{\it a1}}^{2}{\it b1}\,{x}^{2}-{\it a1}\,{\it a2}\,{\it b1}\,xy \left ( x \right ) +3\,{\it a2}\,{\it b0}\,{\it b1}\,xy \left ( x \right ) \right ) } \right ) ^{-{\frac {2\,{\it a2}+{\it b1}}{2\,{\it a2}+2\,{\it b1}}}}{{\rm e}^{2\,{\frac {{\it a1}\,{\it a2}}{\sqrt {4\,{\it a0}\,{\it a2}+4\,{\it a0}\,{\it b1}-{{\it a1}}^{2}-2\,{\it a1}\,{\it b0}-{{\it b0}}^{2}} \left ( {\it a2}+{\it b1} \right ) }\arctan \left ( {\frac {-{\it a1}\,{\it b1}\,x+{\it a2}\,{\it b0}\,x-{\it a2}\,{\it b1}\,y \left ( x \right ) -{{\it b1}}^{2}y \left ( x \right ) +\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it a2}+\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it b1}+{\it a1}\,{\it c2}-{\it a2}\,{\it c1}+{\it b0}\,{\it c2}-{\it b1}\,{\it c1}}{ \left ( {\it a2}\,x+{\it c2} \right ) \sqrt {4\,{\it a0}\,{\it a2}+4\,{\it a0}\,{\it b1}-{{\it a1}}^{2}-2\,{\it a1}\,{\it b0}-{{\it b0}}^{2}}}} \right ) }+{\frac {{\it b1}\,{\it a1}}{{\it a2}+{\it b1}}\arctan \left ( {\frac {1}{{\it a2}\,x+{\it c2}} \left ( -{\it a1}\,{\it b1}\,x+{\it a2}\,{\it b0}\,x-{\it a2}\,{\it b1}\,y \left ( x \right ) -{{\it b1}}^{2}y \left ( x \right ) +\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it a2}+\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it b1}+{\it a1}\,{\it c2}-{\it a2}\,{\it c1}+{\it b0}\,{\it c2}-{\it b1}\,{\it c1} \right ) {\frac {1}{\sqrt {4\,{\it a0}\,{\it a2}+4\,{\it a0}\,{\it b1}-{{\it a1}}^{2}-2\,{\it a1}\,{\it b0}-{{\it b0}}^{2}}}}} \right ) {\frac {1}{\sqrt {4\,{\it a0}\,{\it a2}+4\,{\it a0}\,{\it b1}-{{\it a1}}^{2}-2\,{\it a1}\,{\it b0}-{{\it b0}}^{2}}}}}+2\,{\frac {{\it b0}\,{\it a2}}{\sqrt {4\,{\it a0}\,{\it a2}+4\,{\it a0}\,{\it b1}-{{\it a1}}^{2}-2\,{\it a1}\,{\it b0}-{{\it b0}}^{2}} \left ( {\it a2}+{\it b1} \right ) }\arctan \left ( {\frac {-{\it a1}\,{\it b1}\,x+{\it a2}\,{\it b0}\,x-{\it a2}\,{\it b1}\,y \left ( x \right ) -{{\it b1}}^{2}y \left ( x \right ) +\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it a2}+\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it b1}+{\it a1}\,{\it c2}-{\it a2}\,{\it c1}+{\it b0}\,{\it c2}-{\it b1}\,{\it c1}}{ \left ( {\it a2}\,x+{\it c2} \right ) \sqrt {4\,{\it a0}\,{\it a2}+4\,{\it a0}\,{\it b1}-{{\it a1}}^{2}-2\,{\it a1}\,{\it b0}-{{\it b0}}^{2}}}} \right ) }+{\frac {{\it b1}\,{\it b0}}{{\it a2}+{\it b1}}\arctan \left ( {\frac {1}{{\it a2}\,x+{\it c2}} \left ( -{\it a1}\,{\it b1}\,x+{\it a2}\,{\it b0}\,x-{\it a2}\,{\it b1}\,y \left ( x \right ) -{{\it b1}}^{2}y \left ( x \right ) +\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it a2}+\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it b1}+{\it a1}\,{\it c2}-{\it a2}\,{\it c1}+{\it b0}\,{\it c2}-{\it b1}\,{\it c1} \right ) {\frac {1}{\sqrt {4\,{\it a0}\,{\it a2}+4\,{\it a0}\,{\it b1}-{{\it a1}}^{2}-2\,{\it a1}\,{\it b0}-{{\it b0}}^{2}}}}} \right ) {\frac {1}{\sqrt {4\,{\it a0}\,{\it a2}+4\,{\it a0}\,{\it b1}-{{\it a1}}^{2}-2\,{\it a1}\,{\it b0}-{{\it b0}}^{2}}}}}-2\,{\frac {{\it a1}}{\sqrt {4\,{\it a0}\,{\it a2}+4\,{\it a0}\,{\it b1}-{{\it a1}}^{2}-2\,{\it a1}\,{\it b0}-{{\it b0}}^{2}}}\arctan \left ( {\frac {-{\it a1}\,{\it b1}\,x+{\it a2}\,{\it b0}\,x-{\it a2}\,{\it b1}\,y \left ( x \right ) -{{\it b1}}^{2}y \left ( x \right ) +\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it a2}+\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it b1}+{\it a1}\,{\it c2}-{\it a2}\,{\it c1}+{\it b0}\,{\it c2}-{\it b1}\,{\it c1}}{ \left ( {\it a2}\,x+{\it c2} \right ) \sqrt {4\,{\it a0}\,{\it a2}+4\,{\it a0}\,{\it b1}-{{\it a1}}^{2}-2\,{\it a1}\,{\it b0}-{{\it b0}}^{2}}}} \right ) }}}}+x-{\frac {1}{2\,{\it a2}\,x+2\,{\it c2}}\int ^{{\frac {1}{2\,{\it a2}\,x+2\,{\it c2}} \left ( -{\it a1}\,x-{\it b1}\,y \left ( x \right ) -{\it c1}+\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}} \right ) }}\!-{\frac {{{\it \_a}}^{2}{\it b1}\,{\it c2}+2\,{\it \_a}\,{\it b0}\,{\it c2}+{\it b0}\,{\it c1}-{\it b1}\,{\it c0}}{ \left ( {\it \_a}\,{\it b1}+{\it b0} \right ) ^{2}} \left ( {{\it \_a}}^{2}{\it a2}+{{\it \_a}}^{2}{\it b1}+{\it \_a}\,{\it a1}+{\it \_a}\,{\it b0}+{\it a0} \right ) ^{-{\frac {{\it b1}}{2\,{\it a2}+2\,{\it b1}}}}{{\rm e}^{2\,{\frac {{\it a1}}{\sqrt {4\,{\it a0}\,{\it a2}+4\,{\it a0}\,{\it b1}-{{\it a1}}^{2}-2\,{\it a1}\,{\it b0}-{{\it b0}}^{2}}}\arctan \left ( {\frac {2\,{\it \_a}\,{\it a2}+2\,{\it \_a}\,{\it b1}+{\it a1}+{\it b0}}{\sqrt {4\,{\it a0}\,{\it a2}+4\,{\it a0}\,{\it b1}-{{\it a1}}^{2}-2\,{\it a1}\,{\it b0}-{{\it b0}}^{2}}}} \right ) }-{\frac {{\it b1}\,{\it b0}}{{\it a2}+{\it b1}}\arctan \left ( {(2\,{\it \_a}\,{\it a2}+2\,{\it \_a}\,{\it b1}+{\it a1}+{\it b0}){\frac {1}{\sqrt {4\,{\it a0}\,{\it a2}+4\,{\it a0}\,{\it b1}-{{\it a1}}^{2}-2\,{\it a1}\,{\it b0}-{{\it b0}}^{2}}}}} \right ) {\frac {1}{\sqrt {4\,{\it a0}\,{\it a2}+4\,{\it a0}\,{\it b1}-{{\it a1}}^{2}-2\,{\it a1}\,{\it b0}-{{\it b0}}^{2}}}}}-2\,{\frac {{\it b0}\,{\it a2}}{\sqrt {4\,{\it a0}\,{\it a2}+4\,{\it a0}\,{\it b1}-{{\it a1}}^{2}-2\,{\it a1}\,{\it b0}-{{\it b0}}^{2}} \left ( {\it a2}+{\it b1} \right ) }\arctan \left ( {\frac {2\,{\it \_a}\,{\it a2}+2\,{\it \_a}\,{\it b1}+{\it a1}+{\it b0}}{\sqrt {4\,{\it a0}\,{\it a2}+4\,{\it a0}\,{\it b1}-{{\it a1}}^{2}-2\,{\it a1}\,{\it b0}-{{\it b0}}^{2}}}} \right ) }-{\frac {{\it b1}\,{\it a1}}{{\it a2}+{\it b1}}\arctan \left ( {(2\,{\it \_a}\,{\it a2}+2\,{\it \_a}\,{\it b1}+{\it a1}+{\it b0}){\frac {1}{\sqrt {4\,{\it a0}\,{\it a2}+4\,{\it a0}\,{\it b1}-{{\it a1}}^{2}-2\,{\it a1}\,{\it b0}-{{\it b0}}^{2}}}}} \right ) {\frac {1}{\sqrt {4\,{\it a0}\,{\it a2}+4\,{\it a0}\,{\it b1}-{{\it a1}}^{2}-2\,{\it a1}\,{\it b0}-{{\it b0}}^{2}}}}}-2\,{\frac {{\it a1}\,{\it a2}}{\sqrt {4\,{\it a0}\,{\it a2}+4\,{\it a0}\,{\it b1}-{{\it a1}}^{2}-2\,{\it a1}\,{\it b0}-{{\it b0}}^{2}} \left ( {\it a2}+{\it b1} \right ) }\arctan \left ( {\frac {2\,{\it \_a}\,{\it a2}+2\,{\it \_a}\,{\it b1}+{\it a1}+{\it b0}}{\sqrt {4\,{\it a0}\,{\it a2}+4\,{\it a0}\,{\it b1}-{{\it a1}}^{2}-2\,{\it a1}\,{\it b0}-{{\it b0}}^{2}}}} \right ) }}}}{d{\it \_a}} \left ( -{\it a1}\,{\it b1}\,x+2\,{\it a2}\,{\it b0}\,x-{{\it b1}}^{2}y \left ( x \right ) +\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it b1}+2\,{\it b0}\,{\it c2}-{\it b1}\,{\it c1} \right ) \left ( -{\frac {1}{2\, \left ( {\it a2}\,x+{\it c2} \right ) ^{2}} \left ( -{\it a1}\,{\it a2}\,{\it c1}\,x-2\,{\it a1}\,{\it b1}\,{\it c1}\,x+{\it a1}\,{\it a2}\,{\it b0}\,{x}^{2}+{\it a1}\,{\it b0}\,{\it c2}\,x+{\it a2}\,{\it b0}\,{\it c1}\,x-2\,{\it a0}\,{\it a2}\,{\it c2}\,x+2\,{\it a0}\,{\it a2}\,{\it b1}\,{x}^{2}-{{\it b1}}^{3} \left ( y \left ( x \right ) \right ) ^{2}-{\it a2}\,{{\it c1}}^{2}-{\it b1}\,{{\it c1}}^{2}-2\,{\it a0}\,{{\it c2}}^{2}-2\,{\it a2}\,{\it b1}\,{\it c1}\,y \left ( x \right ) -2\,{\it a1}\,{{\it b1}}^{2}xy \left ( x \right ) +{\it a1}\,{\it b1}\,{\it c2}\,y \left ( x \right ) +3\,{\it b0}\,{\it b1}\,{\it c2}\,y \left ( x \right ) +\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it a1}\,{\it b1}\,x-\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it a2}\,{\it b0}\,x+\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it a2}\,{\it b1}\,y \left ( x \right ) +2\,{{\it a2}}^{2}{\it b0}\,xy \left ( x \right ) +2\,{\it a2}\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it a0}\,{\it b1}\,{\it c2}\,x+2\,{\it a2}\,{\it b1}\,{\it c0}\,x-2\,{{\it b1}}^{2}{\it c1}\,y \left ( x \right ) +\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{{\it b1}}^{2}y \left ( x \right ) -\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it a1}\,{\it c2}+\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it a2}\,{\it c1}-\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it b0}\,{\it c2}+\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it b1}\,{\it c1}-{\it a2}\,{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}+{{\it a1}}^{2}{\it c2}\,x+{\it a1}\,{\it c1}\,{\it c2}+{\it b0}\,{\it c1}\,{\it c2}+2\,{{\it a2}}^{2}{\it c0}\,x+2\,{\it a2}\,{\it c0}\,{\it c2}+2\,{\it b1}\,{\it c0}\,{\it c2}-{{\it a1}}^{2}{\it b1}\,{x}^{2}-{\it a1}\,{\it a2}\,{\it b1}\,xy \left ( x \right ) +3\,{\it a2}\,{\it b0}\,{\it b1}\,xy \left ( x \right ) \right ) } \right ) ^{-{\frac {2\,{\it a2}+{\it b1}}{2\,{\it a2}+2\,{\it b1}}}}{{\rm e}^{2\,{\frac {{\it a1}\,{\it a2}}{\sqrt {4\,{\it a0}\,{\it a2}+4\,{\it a0}\,{\it b1}-{{\it a1}}^{2}-2\,{\it a1}\,{\it b0}-{{\it b0}}^{2}} \left ( {\it a2}+{\it b1} \right ) }\arctan \left ( {\frac {-{\it a1}\,{\it b1}\,x+{\it a2}\,{\it b0}\,x-{\it a2}\,{\it b1}\,y \left ( x \right ) -{{\it b1}}^{2}y \left ( x \right ) +\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it a2}+\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it b1}+{\it a1}\,{\it c2}-{\it a2}\,{\it c1}+{\it b0}\,{\it c2}-{\it b1}\,{\it c1}}{ \left ( {\it a2}\,x+{\it c2} \right ) \sqrt {4\,{\it a0}\,{\it a2}+4\,{\it a0}\,{\it b1}-{{\it a1}}^{2}-2\,{\it a1}\,{\it b0}-{{\it b0}}^{2}}}} \right ) }+{\frac {{\it b1}\,{\it a1}}{{\it a2}+{\it b1}}\arctan \left ( {\frac {1}{{\it a2}\,x+{\it c2}} \left ( -{\it a1}\,{\it b1}\,x+{\it a2}\,{\it b0}\,x-{\it a2}\,{\it b1}\,y \left ( x \right ) -{{\it b1}}^{2}y \left ( x \right ) +\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it a2}+\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it b1}+{\it a1}\,{\it c2}-{\it a2}\,{\it c1}+{\it b0}\,{\it c2}-{\it b1}\,{\it c1} \right ) {\frac {1}{\sqrt {4\,{\it a0}\,{\it a2}+4\,{\it a0}\,{\it b1}-{{\it a1}}^{2}-2\,{\it a1}\,{\it b0}-{{\it b0}}^{2}}}}} \right ) {\frac {1}{\sqrt {4\,{\it a0}\,{\it a2}+4\,{\it a0}\,{\it b1}-{{\it a1}}^{2}-2\,{\it a1}\,{\it b0}-{{\it b0}}^{2}}}}}+2\,{\frac {{\it b0}\,{\it a2}}{\sqrt {4\,{\it a0}\,{\it a2}+4\,{\it a0}\,{\it b1}-{{\it a1}}^{2}-2\,{\it a1}\,{\it b0}-{{\it b0}}^{2}} \left ( {\it a2}+{\it b1} \right ) }\arctan \left ( {\frac {-{\it a1}\,{\it b1}\,x+{\it a2}\,{\it b0}\,x-{\it a2}\,{\it b1}\,y \left ( x \right ) -{{\it b1}}^{2}y \left ( x \right ) +\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it a2}+\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it b1}+{\it a1}\,{\it c2}-{\it a2}\,{\it c1}+{\it b0}\,{\it c2}-{\it b1}\,{\it c1}}{ \left ( {\it a2}\,x+{\it c2} \right ) \sqrt {4\,{\it a0}\,{\it a2}+4\,{\it a0}\,{\it b1}-{{\it a1}}^{2}-2\,{\it a1}\,{\it b0}-{{\it b0}}^{2}}}} \right ) }+{\frac {{\it b1}\,{\it b0}}{{\it a2}+{\it b1}}\arctan \left ( {\frac {1}{{\it a2}\,x+{\it c2}} \left ( -{\it a1}\,{\it b1}\,x+{\it a2}\,{\it b0}\,x-{\it a2}\,{\it b1}\,y \left ( x \right ) -{{\it b1}}^{2}y \left ( x \right ) +\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it a2}+\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it b1}+{\it a1}\,{\it c2}-{\it a2}\,{\it c1}+{\it b0}\,{\it c2}-{\it b1}\,{\it c1} \right ) {\frac {1}{\sqrt {4\,{\it a0}\,{\it a2}+4\,{\it a0}\,{\it b1}-{{\it a1}}^{2}-2\,{\it a1}\,{\it b0}-{{\it b0}}^{2}}}}} \right ) {\frac {1}{\sqrt {4\,{\it a0}\,{\it a2}+4\,{\it a0}\,{\it b1}-{{\it a1}}^{2}-2\,{\it a1}\,{\it b0}-{{\it b0}}^{2}}}}}-2\,{\frac {{\it a1}}{\sqrt {4\,{\it a0}\,{\it a2}+4\,{\it a0}\,{\it b1}-{{\it a1}}^{2}-2\,{\it a1}\,{\it b0}-{{\it b0}}^{2}}}\arctan \left ( {\frac {-{\it a1}\,{\it b1}\,x+{\it a2}\,{\it b0}\,x-{\it a2}\,{\it b1}\,y \left ( x \right ) -{{\it b1}}^{2}y \left ( x \right ) +\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it a2}+\sqrt {-4\,{\it a0}\,{\it a2}\,{x}^{2}+{{\it a1}}^{2}{x}^{2}+2\,{\it a1}\,{\it b1}\,xy \left ( x \right ) -4\,{\it a2}\,{\it b0}\,xy \left ( x \right ) +{{\it b1}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\,{\it a0}\,{\it c2}\,x+2\,{\it a1}\,{\it c1}\,x-4\,{\it a2}\,{\it c0}\,x-4\,{\it b0}\,{\it c2}\,y \left ( x \right ) +2\,{\it b1}\,{\it c1}\,y \left ( x \right ) -4\,{\it c0}\,{\it c2}+{{\it c1}}^{2}}{\it b1}+{\it a1}\,{\it c2}-{\it a2}\,{\it c1}+{\it b0}\,{\it c2}-{\it b1}\,{\it c1}}{ \left ( {\it a2}\,x+{\it c2} \right ) \sqrt {4\,{\it a0}\,{\it a2}+4\,{\it a0}\,{\it b1}-{{\it a1}}^{2}-2\,{\it a1}\,{\it b0}-{{\it b0}}^{2}}}} \right ) }}}}=0 \right \} \]