\[ -\text {a0} (a-y(x))^2 (b-y(x))^2 (c-y(x))^2-\text {a2} (a-y(x))^2 (c-y(x))^2-\text {a3} (a-y(x))^2 (b-y(x))^2+2 (a-y(x)) (b-y(x)) (c-y(x)) y''(x)+y'(x)^2 ((a-y(x)) (b-y(x))+(a-y(x)) (c-y(x))+(b-y(x)) (c-y(x)))-\text {a1} (b-y(x))^2 (c-y(x))^2=0 \] ✓ Mathematica : cpu = 17.1006 (sec), leaf count = 10387
DSolve[-(a3*(a - y[x])^2*(b - y[x])^2) - a2*(a - y[x])^2*(c - y[x])^2 - a1*(b - y[x])^2*(c - y[x])^2 - a0*(a - y[x])^2*(b - y[x])^2*(c - y[x])^2 + ((a - y[x])*(b - y[x]) + (a - y[x])*(c - y[x]) + (b - y[x])*(c - y[x]))*Derivative[1][y][x]^2 + 2*(a - y[x])*(b - y[x])*(c - y[x])*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\text {Solve}\left [-\frac {2 \operatorname {EllipticF}\left (\arcsin \left (\sqrt {\frac {\left (\text {Root}\left [\text {a0} \text {$\#$1}^4+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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) (\text {a2}+(b-y(x)) (\text {a0} y(x)-c_1)) (c-y(x))+\text {a3} y(x) (y(x)-b)+a (\text {a3} (b-y(x))+(c-y(x)) (\text {a2}+(b-y(x)) (\text {a0} y(x)-c_1)))}}=x+c_2,y(x)\right ],\text {Solve}\left [\frac {2 \operatorname {EllipticF}\left (\arcsin \left (\sqrt {\frac {\left (\text {Root}\left [\text {a0} \text {$\#$1}^4+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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+(-a \text {a0}-b \text {a0}-c \text {a0}-c_1) \text {$\#$1}^3+(-\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) \text {$\#$1}^2+(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) \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) (\text {a2}+(b-y(x)) (\text {a0} y(x)-c_1)) (c-y(x))+\text {a3} y(x) (y(x)-b)+a (\text {a3} (b-y(x))+(c-y(x)) (\text {a2}+(b-y(x)) (\text {a0} y(x)-c_1)))}}=x+c_2,y(x)\right ]\right \}\] ✓ Maple : cpu = 0.917 (sec), leaf count = 304
dsolve(2*(c-y(x))*(-y(x)+b)*(-y(x)+a)*diff(diff(y(x),x),x)+((-y(x)+a)*(-y(x)+b)+(c-y(x))*(-y(x)+a)+(-y(x)+b)*(c-y(x)))*diff(y(x),x)^2-a0*(c-y(x))^2*(-y(x)+b)^2*(-y(x)+a)^2-a1*(-y(x)+b)^2*(c-y(x))^2-a2*(c-y(x))^2*(-y(x)+a)^2-a3*(-y(x)+b)^2*(-y(x)+a)^2=0,y(x))
\[\int _{}^{y \left (x \right )}\frac {1}{\sqrt {-\operatorname {a0} \,\textit {\_a}^{4}+\operatorname {a0} \,\textit {\_a}^{3} a +\textit {\_a}^{3} \operatorname {a0} b +\textit {\_a}^{3} \operatorname {a0} c -\textit {\_a}^{2} a \operatorname {a0} b -\textit {\_a}^{2} a \operatorname {a0} c -\textit {\_a}^{2} \operatorname {a0} b c +\textit {\_a} a \operatorname {a0} b c +\textit {\_a}^{3} c_{1}-\textit {\_a}^{2} a c_{1}-\textit {\_a}^{2} b c_{1}-\textit {\_a}^{2} c c_{1}+\textit {\_a} a b c_{1}+\textit {\_a} a c c_{1}+\textit {\_a} b c c_{1}-a b c c_{1}+\textit {\_a}^{2} \operatorname {a1} +\textit {\_a}^{2} \operatorname {a2} +\textit {\_a}^{2} \operatorname {a3} -\textit {\_a} a \operatorname {a2} -\textit {\_a} a \operatorname {a3} -\textit {\_a} \operatorname {a1} b -\textit {\_a} \operatorname {a1} c -\textit {\_a} \operatorname {a2} c -\textit {\_a} \operatorname {a3} b +a \operatorname {a2} c +a \operatorname {a3} b +b c \operatorname {a1}}}d \textit {\_a} -x -c_{2} = 0\]