\[ \boxed { 2\, \left ( c-y \left ( x \right ) \right ) \left ( -y \left ( x \right ) +b \right ) \left ( -y \left ( x \right ) +a \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) + \left ( \left ( -y \left ( x \right ) +a \right ) \left ( -y \left ( x \right ) +b \right ) + \left ( c-y \left ( x \right ) \right ) \left ( -y \left ( x \right ) +a \right ) + \left ( -y \left ( x \right ) +b \right ) \left ( c-y \left ( x \right ) \right ) \right ) \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}-{\it a0}\, \left ( c-y \left ( x \right ) \right ) ^{2} \left ( -y \left ( x \right ) +b \right ) ^{2} \left ( -y \left ( x \right ) +a \right ) ^{2}-{\it a1}\, \left ( -y \left ( x \right ) +b \right ) ^{2} \left ( c-y \left ( x \right ) \right ) ^{2}-{\it a2}\, \left ( c-y \left ( x \right ) \right ) ^{2} \left ( -y \left ( x \right ) +a \right ) ^{2}-{\it a3}\, \left ( -y \left ( x \right ) +b \right ) ^{2} \left ( -y \left ( x \right ) +a \right ) ^{2}=0} \]
Mathematica: cpu = 18.332328 (sec), leaf count = 10387 \[ \left \{\text {Solve}\left [-\frac {2 F\left (\sin ^{-1}\left (\sqrt {\frac {\left (\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,2\right ]-\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,4\right ]\right ) \left (y(x)-\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,1\right ]\right )}{\left (\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,1\right ]-\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,4\right ]\right ) \left (y(x)-\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,2\right ]\right )}}\right )|\frac {\left (\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,2\right ]-\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,3\right ]\right ) \left (\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,1\right ]-\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,4\right ]\right )}{\left (\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,1\right ]-\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,3\right ]\right ) \left (\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,2\right ]-\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,4\right ]\right )}\right ) \left (\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,1\right ]-\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,4\right ]\right ) \left (y(x)-\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,2\right ]\right ){}^2 \sqrt {\frac {\left (\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,1\right ]-\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,2\right ]\right ) \left (y(x)-\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,3\right ]\right )}{\left (\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,1\right ]-\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,3\right ]\right ) \left (y(x)-\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,2\right ]\right )}} \sqrt {\frac {\left (\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,1\right ]-\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,2\right ]\right ) \left (\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,2\right ]-\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,4\right ]\right ) \left (y(x)-\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,1\right ]\right ) \left (y(x)-\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,4\right ]\right )}{\left (\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,1\right ]-\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,4\right ]\right ){}^2 \left (y(x)-\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,2\right ]\right ){}^2}}}{\left (\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,2\right ]-\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,1\right ]\right ) \left (\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,2\right ]-\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,4\right ]\right ) \sqrt {\text {a1} (b-y(x)) (c-y(x))+y(x) \left (\text {a3} (y(x)-b)-(c-y(x)) \left (\text {a2}+(b-y(x)) \left (\text {a0} y(x)-c_1\right )\right )\right )+a \left (\text {a3} (b-y(x))+(c-y(x)) \left (\text {a2}+(b-y(x)) \left (\text {a0} y(x)-c_1\right )\right )\right )}}=x+c_2,y(x)\right ],\text {Solve}\left [\frac {2 F\left (\sin ^{-1}\left (\sqrt {\frac {\left (\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,2\right ]-\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,4\right ]\right ) \left (y(x)-\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,1\right ]\right )}{\left (\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,1\right ]-\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,4\right ]\right ) \left (y(x)-\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,2\right ]\right )}}\right )|\frac {\left (\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,2\right ]-\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,3\right ]\right ) \left (\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,1\right ]-\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,4\right ]\right )}{\left (\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,1\right ]-\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,3\right ]\right ) \left (\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,2\right ]-\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,4\right ]\right )}\right ) \left (\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,1\right ]-\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,4\right ]\right ) \left (y(x)-\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,2\right ]\right ){}^2 \sqrt {\frac {\left (\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,1\right ]-\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,2\right ]\right ) \left (y(x)-\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,3\right ]\right )}{\left (\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,1\right ]-\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,3\right ]\right ) \left (y(x)-\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,2\right ]\right )}} \sqrt {\frac {\left (\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,1\right ]-\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,2\right ]\right ) \left (\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,2\right ]-\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,4\right ]\right ) \left (y(x)-\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,1\right ]\right ) \left (y(x)-\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,4\right ]\right )}{\left (\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,1\right ]-\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,4\right ]\right ){}^2 \left (y(x)-\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,2\right ]\right ){}^2}}}{\left (\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,2\right ]-\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,1\right ]\right ) \left (\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,2\right ]-\text {Root}\left [\text {a0} \text {$\#$1}^4+\left (-a \text {a0}-b \text {a0}-c \text {a0}-c_1\right ) \text {$\#$1}^3+\left (-\text {a1}-\text {a2}-\text {a3}+a \text {a0} b+a \text {a0} c+\text {a0} b c+a c_1+b c_1+c c_1\right ) \text {$\#$1}^2+\left (a \text {a2}+c \text {a2}+a \text {a3}+\text {a1} b+\text {a3} b+\text {a1} c-a \text {a0} b c-a b c_1-a c c_1-b c c_1\right ) \text {$\#$1}-a \text {a3} b-a \text {a2} c-\text {a1} b c+a b c c_1\& ,4\right ]\right ) \sqrt {\text {a1} (b-y(x)) (c-y(x))+y(x) \left (\text {a3} (y(x)-b)-(c-y(x)) \left (\text {a2}+(b-y(x)) \left (\text {a0} y(x)-c_1\right )\right )\right )+a \left (\text {a3} (b-y(x))+(c-y(x)) \left (\text {a2}+(b-y(x)) \left (\text {a0} y(x)-c_1\right )\right )\right )}}=x+c_2,y(x)\right ]\right \} \]
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