ODE
\[ 2 (a-y(x)) (b-y(x)) (c-y(x)) y''(x)+y'(x)^2 ((a-y(x)) (b-y(x))+(a-y(x)) (c-y(x))+(b-y(x)) (c-y(x)))=\text {a0} (a-y(x))^2 (b-y(x))^2 (c-y(x))^2+2 \text {a2} (a-y(x))^2 (c-y(x))^2+\text {a3} (a-y(x))^2 (b-y(x))^2+\text {a1} (b-y(x))^2 (c-y(x))^2 \] ODE Classification
[[_2nd_order, _missing_x]]
Book solution method
TO DO
Mathematica ✓
cpu = 20.6728 (sec), leaf count = 10112
\[\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}-2 \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 (2 a \text {a2}+2 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-2 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}-2 \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 (2 a \text {a2}+2 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-2 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}-2 \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 (2 a \text {a2}+2 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-2 a \text {a2} c-\text {a1} b c+a b c c_1\& ,1\right ]-y(x)\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}-2 \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 (2 a \text {a2}+2 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-2 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}-2 \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 (2 a \text {a2}+2 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-2 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}-2 \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 (2 a \text {a2}+2 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-2 a \text {a2} c-\text {a1} b c+a b c c_1\& ,2\right ]-y(x)\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}-2 \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 (2 a \text {a2}+2 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-2 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}-2 \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 (2 a \text {a2}+2 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-2 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}-2 \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 (2 a \text {a2}+2 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-2 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}-2 \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 (2 a \text {a2}+2 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-2 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}-2 \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 (2 a \text {a2}+2 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-2 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}-2 \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 (2 a \text {a2}+2 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-2 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}-2 \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 (2 a \text {a2}+2 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-2 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}-2 \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 (2 a \text {a2}+2 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-2 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}-2 \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 (2 a \text {a2}+2 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-2 a \text {a2} c-\text {a1} b c+a b c c_1\& ,1\right ]-y(x)\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}-2 \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 (2 a \text {a2}+2 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-2 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}-2 \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 (2 a \text {a2}+2 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-2 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}-2 \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 (2 a \text {a2}+2 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-2 a \text {a2} c-\text {a1} b c+a b c c_1\& ,3\right ]-y(x)\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}-2 \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 (2 a \text {a2}+2 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-2 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}-2 \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 (2 a \text {a2}+2 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-2 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}-2 \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 (2 a \text {a2}+2 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-2 a \text {a2} c-\text {a1} b c+a b c c_1\& ,2\right ]-y(x)\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}-2 \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 (2 a \text {a2}+2 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-2 a \text {a2} c-\text {a1} b c+a b c c_1\& ,4\right ]-y(x)\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}-2 \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 (2 a \text {a2}+2 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-2 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}-2 \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 (2 a \text {a2}+2 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-2 a \text {a2} c-\text {a1} b c+a b c c_1\& ,4\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}-2 \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 (2 a \text {a2}+2 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-2 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}-2 \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 (2 a \text {a2}+2 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-2 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}-2 \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 (2 a \text {a2}+2 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-2 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}-2 \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 (2 a \text {a2}+2 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-2 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}-2 \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 (2 a \text {a2}+2 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-2 a \text {a2} c-\text {a1} b c+a b c c_1\& ,1\right ]-y(x)\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}-2 \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 (2 a \text {a2}+2 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-2 a \text {a2} c-\text {a1} b c+a b c c_1\& ,4\right ]-y(x)\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}-2 \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 (2 a \text {a2}+2 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-2 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}-2 \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 (2 a \text {a2}+2 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-2 a \text {a2} c-\text {a1} b c+a b c c_1\& ,4\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}-2 \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 (2 a \text {a2}+2 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-2 a \text {a2} c-\text {a1} b c+a b c c_1\& ,2\right ]-y(x)\right ){}^2}} \sqrt {\text {a1} (b-y(x)) (c-y(x))+a \left (\text {a3} (b-y(x))+(c-y(x)) \left (2 \text {a2}+(b-y(x)) \left (\text {a0} y(x)-c_1\right )\right )\right )+y(x) \left (\text {a3} (y(x)-b)+(c-y(x)) \left ((y(x)-b) \left (\text {a0} y(x)-c_1\right )-2 \text {a2}\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}-2 \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 (2 a \text {a2}+2 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-2 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}-2 \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 (2 a \text {a2}+2 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-2 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}-2 \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 (2 a \text {a2}+2 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-2 a \text {a2} c-\text {a1} b c+a b c c_1\& ,1\right ]-y(x)\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}-2 \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 (2 a \text {a2}+2 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-2 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}-2 \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 (2 a \text {a2}+2 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-2 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}-2 \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 (2 a \text {a2}+2 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-2 a \text {a2} c-\text {a1} b c+a b c c_1\& ,2\right ]-y(x)\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}-2 \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 (2 a \text {a2}+2 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-2 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}-2 \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 (2 a \text {a2}+2 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-2 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}-2 \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 (2 a \text {a2}+2 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-2 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}-2 \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 (2 a \text {a2}+2 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-2 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}-2 \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 (2 a \text {a2}+2 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-2 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}-2 \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 (2 a \text {a2}+2 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-2 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}-2 \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 (2 a \text {a2}+2 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-2 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}-2 \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 (2 a \text {a2}+2 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-2 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}-2 \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 (2 a \text {a2}+2 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-2 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}-2 \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 (2 a \text {a2}+2 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-2 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}-2 \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 (2 a \text {a2}+2 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-2 a \text {a2} c-\text {a1} b c+a b c c_1\& ,2\right ]-y(x)\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}-2 \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 (2 a \text {a2}+2 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-2 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}-2 \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 (2 a \text {a2}+2 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-2 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}-2 \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 (2 a \text {a2}+2 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-2 a \text {a2} c-\text {a1} b c+a b c c_1\& ,3\right ]-y(x)\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}-2 \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 (2 a \text {a2}+2 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-2 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}-2 \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 (2 a \text {a2}+2 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-2 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}-2 \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 (2 a \text {a2}+2 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-2 a \text {a2} c-\text {a1} b c+a b c c_1\& ,2\right ]-y(x)\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}-2 \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 (2 a \text {a2}+2 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-2 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}-2 \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 (2 a \text {a2}+2 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-2 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}-2 \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 (2 a \text {a2}+2 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-2 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}-2 \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 (2 a \text {a2}+2 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-2 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}-2 \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 (2 a \text {a2}+2 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-2 a \text {a2} c-\text {a1} b c+a b c c_1\& ,1\right ]-y(x)\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}-2 \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 (2 a \text {a2}+2 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-2 a \text {a2} c-\text {a1} b c+a b c c_1\& ,4\right ]-y(x)\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}-2 \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 (2 a \text {a2}+2 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-2 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}-2 \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 (2 a \text {a2}+2 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-2 a \text {a2} c-\text {a1} b c+a b c c_1\& ,4\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}-2 \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 (2 a \text {a2}+2 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-2 a \text {a2} c-\text {a1} b c+a b c c_1\& ,2\right ]-y(x)\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}-2 \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 (2 a \text {a2}+2 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-2 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}-2 \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 (2 a \text {a2}+2 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-2 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}-2 \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 (2 a \text {a2}+2 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-2 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}-2 \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 (2 a \text {a2}+2 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-2 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))+a \left (\text {a3} (b-y(x))+(c-y(x)) \left (2 \text {a2}+(b-y(x)) \left (\text {a0} y(x)-c_1\right )\right )\right )+y(x) \left (\text {a3} (y(x)-b)+(c-y(x)) \left ((y(x)-b) \left (\text {a0} y(x)-c_1\right )-2 \text {a2}\right )\right )}}=x+c_2,y(x)\right ]\right \}\]
Maple ✓
cpu = 1.74 (sec), leaf count = 115637
\[\text {result too large to display}\] Mathematica raw input
DSolve[((a - y[x])*(b - y[x]) + (a - y[x])*(c - y[x]) + (b - y[x])*(c - y[x]))*y'[x]^2 + 2*(a - y[x])*(b - y[x])*(c - y[x])*y''[x] == a3*(a - y[x])^2*(b - y[x])^2 + 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,y[x],x]
Mathematica raw output
{Solve[(2*EllipticF[ArcSin[Sqrt[((Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 2] - Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 4])*(Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 1] - y[x]))/((Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 1] - Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 4])*(Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 2] - y[x]))]], ((Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 2] - Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 3])*(Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 1] - Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 4]))/((Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 1] - Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 3])*(Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 2] - Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 4]))]*(Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 1] - y[x])*Sqrt[((Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 1] - Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 2])*(Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 3] - y[x]))/((Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 1] - Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 3])*(Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 2] - y[x]))]*(Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 4] - y[x]))/((Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 1] - Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 4])*Sqrt[((Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 1] - Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 2])*(Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 2] - Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 4])*(Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 1] - y[x])*(Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 4] - y[x]))/((Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 1] - Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 4])^2*(Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 2] - y[x])^2)]*Sqrt[a1*(b - y[x])*(c - y[x]) + a*(a3*(b - y[x]) + (c - y[x])*(2*a2 + (b - y[x])*(-C[1] + a0*y[x]))) + y[x]*(a3*(-b + y[x]) + (c - y[x])*(-2*a2 + (-b + y[x])*(-C[1] + a0*y[x])))]) == x + C[2], y[x]], Solve[(2*EllipticF[ArcSin[Sqrt[((Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 2] - Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 4])*(Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 1] - y[x]))/((Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 1] - Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 4])*(Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 2] - y[x]))]], ((Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 2] - Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 3])*(Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 1] - Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 4]))/((Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 1] - Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 3])*(Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 2] - Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 4]))]*(Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 1] - Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 4])*(Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 2] - y[x])^2*Sqrt[((Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 1] - Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 2])*(Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 3] - y[x]))/((Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 1] - Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 3])*(Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 2] - y[x]))]*Sqrt[((Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 1] - Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 2])*(Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 2] - Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 4])*(Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 1] - y[x])*(Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 4] - y[x]))/((Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 1] - Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 4])^2*(Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 2] - y[x])^2)])/((-Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 1] + Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 2])*(Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 2] - Root[-(a*a3*b) - 2*a*a2*c - a1*b*c + a*b*c*C[1] + (2*a*a2 + a*a3 + a1*b + a3*b + a1*c + 2*a2*c - a*a0*b*c - a*b*C[1] - a*c*C[1] - b*c*C[1])*#1 + (-a1 - 2*a2 - a3 + a*a0*b + a*a0*c + a0*b*c + a*C[1] + b*C[1] + c*C[1])*#1^2 + (-(a*a0) - a0*b - a0*c - C[1])*#1^3 + a0*#1^4 & , 4])*Sqrt[a1*(b - y[x])*(c - y[x]) + a*(a3*(b - y[x]) + (c - y[x])*(2*a2 + (b - y[x])*(-C[1] + a0*y[x]))) + y[x]*(a3*(-b + y[x]) + (c - y[x])*(-2*a2 + (-b + y[x])*(-C[1] + a0*y[x])))]) == x + C[2], y[x]]}
Maple raw input
dsolve(2*(a-y(x))*(b-y(x))*(c-y(x))*diff(diff(y(x),x),x)+((a-y(x))*(b-y(x))+(a-y(x))*(c-y(x))+(b-y(x))*(c-y(x)))*diff(y(x),x)^2 = a0*(a-y(x))^2*(b-y(x))^2*(c-y(x))^2+a1*(b-y(x))^2*(c-y(x))^2+2*a2*(a-y(x))^2*(c-y(x))^2+a3*(a-y(x))^2*(b-y(x))^2, y(x),'implicit')
Maple raw output
Intat(1/(-_a*a*a0*b*(_a-a^6/(a-c)^2/(a-b)^2/(-a+_a)-b^6/(b-c)^2/(a-b)^2/(-b+_a)+2*a^7/(a-c)^3/(a-b)^3*ln(-a+_a)-4*a^6/(a-c)^3/(a-b)^3*ln(-a+_a)*b-4*a^6/(a-c)^3/(a-b)^3*ln(-a+_a)*c+6*a^5/(a-c)^3/(a-b)^3*ln(-a+_a)*c*b-c^6/(b-c)^2/(a-c)^2/(-c+_a)+4*b^6/(b-c)^3/(a-b)^3*ln(-b+_a)*a-6*b^5/(b-c)^3/(a-b)^3*ln(-b+_a)*c*a-2*b^7/(b-c)^3/(a-b)^3*ln(-b+_a)+4*b^6/(b-c)^3/(a-b)^3*ln(-b+_a)*c+6*c^5/(b-c)^3/(a-c)^3*ln(-c+_a)*a*b-4*c^6/(b-c)^3/(a-c)^3*ln(-c+_a)*a-4*c^6/(b-c)^3/(a-c)^3*ln(-c+_a)*b+2*c^7/(b-c)^3/(a-c)^3*ln(-c+_a))+_a^2*a^2*a3*b^3*(-1/(a-c)^2/(a-b)^2/(-a+_a)-4/(a-c)^3/(a-b)^3*ln(-a+_a)*a+2/(a-c)^3/(a-b)^3*ln(-a+_a)*c+2/(a-c)^3/(a-b)^3*ln(-a+_a)*b-1/(b-c)^2/(a-c)^2/(-c+_a)+4/(b-c)^3/(a-b)^3*ln(-b+_a)*b-2/(b-c)^3/(a-b)^3*ln(-b+_a)*c-2/(b-c)^3/(a-b)^3*ln(-b+_a)*a+2/(b-c)^3/(a-c)^3*ln(-c+_a)*b-4/(b-c)^3/(a-c)^3*ln(-c+_a)*c+2/(b-c)^3/(a-c)^3*ln(-c+_a)*a-1/(b-c)^2/(a-b)^2/(-b+_a))+_a^2*a1*b^3*c^2*(-1/(a-c)^2/(a-b)^2/(-a+_a)-4/(a-c)^3/(a-b)^3*ln(-a+_a)*a+2/(a-c)^3/(a-b)^3*ln(-a+_a)*c+2/(a-c)^3/(a-b)^3*ln(-a+_a)*b-1/(b-c)^2/(a-c)^2/(-c+_a)+4/(b-c)^3/(a-b)^3*ln(-b+_a)*b-2/(b-c)^3/(a-b)^3*ln(-b+_a)*c-2/(b-c)^3/(a-b)^3*ln(-b+_a)*a+2/(b-c)^3/(a-c)^3*ln(-c+_a)*b-4/(b-c)^3/(a-c)^3*ln(-c+_a)*c+2/(b-c)^3/(a-c)^3*ln(-c+_a)*a-1/(b-c)^2/(a-b)^2/(-b+_a))+_a^2*a1*b^2*c^3*(-1/(a-c)^2/(a-b)^2/(-a+_a)-4/(a-c)^3/(a-b)^3*ln(-a+_a)*a+2/(a-c)^3/(a-b)^3*ln(-a+_a)*c+2/(a-c)^3/(a-b)^3*ln(-a+_a)*b-1/(b-c)^2/(a-c)^2/(-c+_a)+4/(b-c)^3/(a-b)^3*ln(-b+_a)*b-2/(b-c)^3/(a-b)^3*ln(-b+_a)*c-2/(b-c)^3/(a-b)^3*ln(-b+_a)*a+2/(b-c)^3/(a-c)^3*ln(-c+_a)*b-4/(b-c)^3/(a-c)^3*ln(-c+_a)*c+2/(b-c)^3/(a-c)^3*ln(-c+_a)*a-1/(b-c)^2/(a-b)^2/(-b+_a))-2*_a*a^3*a2*c^3*(-1/(a-c)^2/(a-b)^2/(-a+_a)-4/(a-c)^3/(a-b)^3*ln(-a+_a)*a+2/(a-c)^3/(a-b)^3*ln(-a+_a)*c+2/(a-c)^3/(a-b)^3*ln(-a+_a)*b-1/(b-c)^2/(a-c)^2/(-c+_a)+4/(b-c)^3/(a-b)^3*ln(-b+_a)*b-2/(b-c)^3/(a-b)^3*ln(-b+_a)*c-2/(b-c)^3/(a-b)^3*ln(-b+_a)*a+2/(b-c)^3/(a-c)^3*ln(-c+_a)*b-4/(b-c)^3/(a-c)^3*ln(-c+_a)*c+2/(b-c)^3/(a-c)^3*ln(-c+_a)*a-1/(b-c)^2/(a-b)^2/(-b+_a))-_a*a^3*a3*b^3*(-1/(a-c)^2/(a-b)^2/(-a+_a)-4/(a-c)^3/(a-b)^3*ln(-a+_a)*a+2/(a-c)^3/(a-b)^3*ln(-a+_a)*c+2/(a-c)^3/(a-b)^3*ln(-a+_a)*b-1/(b-c)^2/(a-c)^2/(-c+_a)+4/(b-c)^3/(a-b)^3*ln(-b+_a)*b-2/(b-c)^3/(a-b)^3*ln(-b+_a)*c-2/(b-c)^3/(a-b)^3*ln(-b+_a)*a+2/(b-c)^3/(a-c)^3*ln(-c+_a)*b-4/(b-c)^3/(a-c)^3*ln(-c+_a)*c+2/(b-c)^3/(a-c)^3*ln(-c+_a)*a-1/(b-c)^2/(a-b)^2/(-b+_a))-_a*a1*b^3*c^3*(-1/(a-c)^2/(a-b)^2/(-a+_a)-4/(a-c)^3/(a-b)^3*ln(-a+_a)*a+2/(a-c)^3/(a-b)^3*ln(-a+_a)*c+2/(a-c)^3/(a-b)^3*ln(-a+_a)*b-1/(b-c)^2/(a-c)^2/(-c+_a)+4/(b-c)^3/(a-b)^3*ln(-b+_a)*b-2/(b-c)^3/(a-b)^3*ln(-b+_a)*c-2/(b-c)^3/(a-b)^3*ln(-b+_a)*a+2/(b-c)^3/(a-c)^3*ln(-c+_a)*b-4/(b-c)^3/(a-c)^3*ln(-c+_a)*c+2/(b-c)^3/(a-c)^3*ln(-c+_a)*a-1/(b-c)^2/(a-b)^2/(-b+_a))+2*a^3*a2*b*c^3*(-1/(a-c)^2/(a-b)^2/(-a+_a)-4/(a-c)^3/(a-b)^3*ln(-a+_a)*a+2/(a-c)^3/(a-b)^3*ln(-a+_a)*c+2/(a-c)^3/(a-b)^3*ln(-a+_a)*b-1/(b-c)^2/(a-c)^2/(-c+_a)+4/(b-c)^3/(a-b)^3*ln(-b+_a)*b-2/(b-c)^3/(a-b)^3*ln(-b+_a)*c-2/(b-c)^3/(a-b)^3*ln(-b+_a)*a+2/(b-c)^3/(a-c)^3*ln(-c+_a)*b-4/(b-c)^3/(a-c)^3*ln(-c+_a)*c+2/(b-c)^3/(a-c)^3*ln(-c+_a)*a-1/(b-c)^2/(a-b)^2/(-b+_a))+a^3*a3*b^3*c*(-1/(a-c)^2/(a-b)^2/(-a+_a)-4/(a-c)^3/(a-b)^3*ln(-a+_a)*a+2/(a-c)^3/(a-b)^3*ln(-a+_a)*c+2/(a-c)^3/(a-b)^3*ln(-a+_a)*b-1/(b-c)^2/(a-c)^2/(-c+_a)+4/(b-c)^3/(a-b)^3*ln(-b+_a)*b-2/(b-c)^3/(a-b)^3*ln(-b+_a)*c-2/(b-c)^3/(a-b)^3*ln(-b+_a)*a+2/(b-c)^3/(a-c)^3*ln(-c+_a)*b-4/(b-c)^3/(a-c)^3*ln(-c+_a)*c+2/(b-c)^3/(a-c)^3*ln(-c+_a)*a-1/(b-c)^2/(a-b)^2/(-b+_a))+a*a1*b^3*c^3*(-1/(a-c)^2/(a-b)^2/(-a+_a)-4/(a-c)^3/(a-b)^3*ln(-a+_a)*a+2/(a-c)^3/(a-b)^3*ln(-a+_a)*c+2/(a-c)^3/(a-b)^3*ln(-a+_a)*b-1/(b-c)^2/(a-c)^2/(-c+_a)+4/(b-c)^3/(a-b)^3*ln(-b+_a)*b-2/(b-c)^3/(a-b)^3*ln(-b+_a)*c-2/(b-c)^3/(a-b)^3*ln(-b+_a)*a+2/(b-c)^3/(a-c)^3*ln(-c+_a)*b-4/(b-c)^3/(a-c)^3*ln(-c+_a)*c+2/(b-c)^3/(a-c)^3*ln(-c+_a)*a-1/(b-c)^2/(a-b)^2/(-b+_a))+a^3*a0*b^3*c^3*(-1/(a-c)^2/(a-b)^2/(-a+_a)-4/(a-c)^3/(a-b)^3*ln(-a+_a)*a+2/(a-c)^3/(a-b)^3*ln(-a+_a)*c+2/(a-c)^3/(a-b)^3*ln(-a+_a)*b-1/(b-c)^2/(a-c)^2/(-c+_a)+4/(b-c)^3/(a-b)^3*ln(-b+_a)*b-2/(b-c)^3/(a-b)^3*ln(-b+_a)*c-2/(b-c)^3/(a-b)^3*ln(-b+_a)*a+2/(b-c)^3/(a-c)^3*ln(-c+_a)*b-4/(b-c)^3/(a-c)^3*ln(-c+_a)*c+2/(b-c)^3/(a-c)^3*ln(-c+_a)*a-1/(b-c)^2/(a-b)^2/(-b+_a))-2*_a^3*a^2*a2*c^2*(-1/(a-c)^2/(a-b)^2/(-a+_a)-4/(a-c)^3/(a-b)^3*ln(-a+_a)*a+2/(a-c)^3/(a-b)^3*ln(-a+_a)*c+2/(a-c)^3/(a-b)^3*ln(-a+_a)*b-1/(b-c)^2/(a-c)^2/(-c+_a)+4/(b-c)^3/(a-b)^3*ln(-b+_a)*b-2/(b-c)^3/(a-b)^3*ln(-b+_a)*c-2/(b-c)^3/(a-b)^3*ln(-b+_a)*a+2/(b-c)^3/(a-c)^3*ln(-c+_a)*b-4/(b-c)^3/(a-c)^3*ln(-c+_a)*c+2/(b-c)^3/(a-c)^3*ln(-c+_a)*a-1/(b-c)^2/(a-b)^2/(-b+_a))-_a^3*a^2*a3*b^2*(-1/(a-c)^2/(a-b)^2/(-a+_a)-4/(a-c)^3/(a-b)^3*ln(-a+_a)*a+2/(a-c)^3/(a-b)^3*ln(-a+_a)*c+2/(a-c)^3/(a-b)^3*ln(-a+_a)*b-1/(b-c)^2/(a-c)^2/(-c+_a)+4/(b-c)^3/(a-b)^3*ln(-b+_a)*b-2/(b-c)^3/(a-b)^3*ln(-b+_a)*c-2/(b-c)^3/(a-b)^3*ln(-b+_a)*a+2/(b-c)^3/(a-c)^3*ln(-c+_a)*b-4/(b-c)^3/(a-c)^3*ln(-c+_a)*c+2/(b-c)^3/(a-c)^3*ln(-c+_a)*a-1/(b-c)^2/(a-b)^2/(-b+_a))-_a^3*a1*b^2*c^2*(-1/(a-c)^2/(a-b)^2/(-a+_a)-4/(a-c)^3/(a-b)^3*ln(-a+_a)*a+2/(a-c)^3/(a-b)^3*ln(-a+_a)*c+2/(a-c)^3/(a-b)^3*ln(-a+_a)*b-1/(b-c)^2/(a-c)^2/(-c+_a)+4/(b-c)^3/(a-b)^3*ln(-b+_a)*b-2/(b-c)^3/(a-b)^3*ln(-b+_a)*c-2/(b-c)^3/(a-b)^3*ln(-b+_a)*a+2/(b-c)^3/(a-c)^3*ln(-c+_a)*b-4/(b-c)^3/(a-c)^3*ln(-c+_a)*c+2/(b-c)^3/(a-c)^3*ln(-c+_a)*a-1/(b-c)^2/(a-b)^2/(-b+_a))+2*_a^2*a^3*a2*c^2*(-1/(a-c)^2/(a-b)^2/(-a+_a)-4/(a-c)^3/(a-b)^3*ln(-a+_a)*a+2/(a-c)^3/(a-b)^3*ln(-a+_a)*c+2/(a-c)^3/(a-b)^3*ln(-a+_a)*b-1/(b-c)^2/(a-c)^2/(-c+_a)+4/(b-c)^3/(a-b)^3*ln(-b+_a)*b-2/(b-c)^3/(a-b)^3*ln(-b+_a)*c-2/(b-c)^3/(a-b)^3*ln(-b+_a)*a+2/(b-c)^3/(a-c)^3*ln(-c+_a)*b-4/(b-c)^3/(a-c)^3*ln(-c+_a)*c+2/(b-c)^3/(a-c)^3*ln(-c+_a)*a-1/(b-c)^2/(a-b)^2/(-b+_a))+_a^2*a^3*a3*b^2*(-1/(a-c)^2/(a-b)^2/(-a+_a)-4/(a-c)^3/(a-b)^3*ln(-a+_a)*a+2/(a-c)^3/(a-b)^3*ln(-a+_a)*c+2/(a-c)^3/(a-b)^3*ln(-a+_a)*b-1/(b-c)^2/(a-c)^2/(-c+_a)+4/(b-c)^3/(a-b)^3*ln(-b+_a)*b-2/(b-c)^3/(a-b)^3*ln(-b+_a)*c-2/(b-c)^3/(a-b)^3*ln(-b+_a)*a+2/(b-c)^3/(a-c)^3*ln(-c+_a)*b-4/(b-c)^3/(a-c)^3*ln(-c+_a)*c+2/(b-c)^3/(a-c)^3*ln(-c+_a)*a-1/(b-c)^2/(a-b)^2/(-b+_a))+2*_a^2*a^2*a2*c^3*(-1/(a-c)^2/(a-b)^2/(-a+_a)-4/(a-c)^3/(a-b)^3*ln(-a+_a)*a+2/(a-c)^3/(a-b)^3*ln(-a+_a)*c+2/(a-c)^3/(a-b)^3*ln(-a+_a)*b-1/(b-c)^2/(a-c)^2/(-c+_a)+4/(b-c)^3/(a-b)^3*ln(-b+_a)*b-2/(b-c)^3/(a-b)^3*ln(-b+_a)*c-2/(b-c)^3/(a-b)^3*ln(-b+_a)*a+2/(b-c)^3/(a-c)^3*ln(-c+_a)*b-4/(b-c)^3/(a-c)^3*ln(-c+_a)*c+2/(b-c)^3/(a-c)^3*ln(-c+_a)*a-1/(b-c)^2/(a-b)^2/(-b+_a))+4*_a^3*a*a2*(-a^3/(a-c)^2/(a-b)^2/(-a+_a)-1/(a-c)^3/(a-b)^3*ln(-a+_a)*a^4-1/(a-c)^3/(a-b)^3*ln(-a+_a)*a^3*b-1/(a-c)^3/(a-b)^3*ln(-a+_a)*a^3*c+3/(a-c)^3/(a-b)^3*ln(-a+_a)*a^2*c*b-c^3/(b-c)^2/(a-c)^2/(-c+_a)+1/(b-c)^3/(a-b)^3*ln(-b+_a)*b^3*a-3/(b-c)^3/(a-b)^3*ln(-b+_a)*b^2*c*a+1/(b-c)^3/(a-b)^3*ln(-b+_a)*b^4+1/(b-c)^3/(a-b)^3*ln(-b+_a)*b^3*c+3/(b-c)^3/(a-c)^3*ln(-c+_a)*c^2*a*b-1/(b-c)^3/(a-c)^3*ln(-c+_a)*c^3*a-1/(b-c)^3/(a-c)^3*ln(-c+_a)*c^3*b-1/(b-c)^3/(a-c)^3*ln(-c+_a)*c^4-b^3/(b-c)^2/(a-b)^2/(-b+_a))+2*_a^3*a*a3*(-a^3/(a-c)^2/(a-b)^2/(-a+_a)-1/(a-c)^3/(a-b)^3*ln(-a+_a)*a^4-1/(a-c)^3/(a-b)^3*ln(-a+_a)*a^3*b-1/(a-c)^3/(a-b)^3*ln(-a+_a)*a^3*c+3/(a-c)^3/(a-b)^3*ln(-a+_a)*a^2*c*b-c^3/(b-c)^2/(a-c)^2/(-c+_a)+1/(b-c)^3/(a-b)^3*ln(-b+_a)*b^3*a-3/(b-c)^3/(a-b)^3*ln(-b+_a)*b^2*c*a+1/(b-c)^3/(a-b)^3*ln(-b+_a)*b^4+1/(b-c)^3/(a-b)^3*ln(-b+_a)*b^3*c+3/(b-c)^3/(a-c)^3*ln(-c+_a)*c^2*a*b-1/(b-c)^3/(a-c)^3*ln(-c+_a)*c^3*a-1/(b-c)^3/(a-c)^3*ln(-c+_a)*c^3*b-1/(b-c)^3/(a-c)^3*ln(-c+_a)*c^4-b^3/(b-c)^2/(a-b)^2/(-b+_a))+2*_a^3*a1*b*(-a^3/(a-c)^2/(a-b)^2/(-a+_a)-1/(a-c)^3/(a-b)^3*ln(-a+_a)*a^4-1/(a-c)^3/(a-b)^3*ln(-a+_a)*a^3*b-1/(a-c)^3/(a-b)^3*ln(-a+_a)*a^3*c+3/(a-c)^3/(a-b)^3*ln(-a+_a)*a^2*c*b-c^3/(b-c)^2/(a-c)^2/(-c+_a)+1/(b-c)^3/(a-b)^3*ln(-b+_a)*b^3*a-3/(b-c)^3/(a-b)^3*ln(-b+_a)*b^2*c*a+1/(b-c)^3/(a-b)^3*ln(-b+_a)*b^4+1/(b-c)^3/(a-b)^3*ln(-b+_a)*b^3*c+3/(b-c)^3/(a-c)^3*ln(-c+_a)*c^2*a*b-1/(b-c)^3/(a-c)^3*ln(-c+_a)*c^3*a-1/(b-c)^3/(a-c)^3*ln(-c+_a)*c^3*b-1/(b-c)^3/(a-c)^3*ln(-c+_a)*c^4-b^3/(b-c)^2/(a-b)^2/(-b+_a))+2*_a^3*a1*c*(-a^3/(a-c)^2/(a-b)^2/(-a+_a)-1/(a-c)^3/(a-b)^3*ln(-a+_a)*a^4-1/(a-c)^3/(a-b)^3*ln(-a+_a)*a^3*b-1/(a-c)^3/(a-b)^3*ln(-a+_a)*a^3*c+3/(a-c)^3/(a-b)^3*ln(-a+_a)*a^2*c*b-c^3/(b-c)^2/(a-c)^2/(-c+_a)+1/(b-c)^3/(a-b)^3*ln(-b+_a)*b^3*a-3/(b-c)^3/(a-b)^3*ln(-b+_a)*b^2*c*a+1/(b-c)^3/(a-b)^3*ln(-b+_a)*b^4+1/(b-c)^3/(a-b)^3*ln(-b+_a)*b^3*c+3/(b-c)^3/(a-c)^3*ln(-c+_a)*c^2*a*b-1/(b-c)^3/(a-c)^3*ln(-c+_a)*c^3*a-1/(b-c)^3/(a-c)^3*ln(-c+_a)*c^3*b-1/(b-c)^3/(a-c)^3*ln(-c+_a)*c^4-b^3/(b-c)^2/(a-b)^2/(-b+_a))+4*_a^3*a2*c*(-a^3/(a-c)^2/(a-b)^2/(-a+_a)-1/(a-c)^3/(a-b)^3*ln(-a+_a)*a^4-1/(a-c)^3/(a-b)^3*ln(-a+_a)*a^3*b-1/(a-c)^3/(a-b)^3*ln(-a+_a)*a^3*c+3/(a-c)^3/(a-b)^3*ln(-a+_a)*a^2*c*b-c^3/(b-c)^2/(a-c)^2/(-c+_a)+1/(b-c)^3/(a-b)^3*ln(-b+_a)*b^3*a-3/(b-c)^3/(a-b)^3*ln(-b+_a)*b^2*c*a+1/(b-c)^3/(a-b)^3*ln(-b+_a)*b^4+1/(b-c)^3/(a-b)^3*ln(-b+_a)*b^3*c+3/(b-c)^3/(a-c)^3*ln(-c+_a)*c^2*a*b-1/(b-c)^3/(a-c)^3*ln(-c+_a)*c^3*a-1/(b-c)^3/(a-c)^3*ln(-c+_a)*c^3*b-1/(b-c)^3/(a-c)^3*ln(-c+_a)*c^4-b^3/(b-c)^2/(a-b)^2/(-b+_a))+2*_a^3*a3*b*(-a^3/(a-c)^2/(a-b)^2/(-a+_a)-1/(a-c)^3/(a-b)^3*ln(-a+_a)*a^4-1/(a-c)^3/(a-b)^3*ln(-a+_a)*a^3*b-1/(a-c)^3/(a-b)^3*ln(-a+_a)*a^3*c+3/(a-c)^3/(a-b)^3*ln(-a+_a)*a^2*c*b-c^3/(b-c)^2/(a-c)^2/(-c+_a)+1/(b-c)^3/(a-b)^3*ln(-b+_a)*b^3*a-3/(b-c)^3/(a-b)^3*ln(-b+_a)*b^2*c*a+1/(b-c)^3/(a-b)^3*ln(-b+_a)*b^4+1/(b-c)^3/(a-b)^3*ln(-b+_a)*b^3*c+3/(b-c)^3/(a-c)^3*ln(-c+_a)*c^2*a*b-1/(b-c)^3/(a-c)^3*ln(-c+_a)*c^3*a-1/(b-c)^3/(a-c)^3*ln(-c+_a)*c^3*b-1/(b-c)^3/(a-c)^3*ln(-c+_a)*c^4-b^3/(b-c)^2/(a-b)^2/(-b+_a))-4*_a^2*a^2*a2*(-a^3/(a-c)^2/(a-b)^2/(-a+_a)-1/(a-c)^3/(a-b)^3*ln(-a+_a)*a^4-1/(a-c)^3/(a-b)^3*ln(-a+_a)*a^3*b-1/(a-c)^3/(a-b)^3*ln(-a+_a)*a^3*c+3/(a-c)^3/(a-b)^3*ln(-a+_a)*a^2*c*b-c^3/(b-c)^2/(a-c)^2/(-c+_a)+1/(b-c)^3/(a-b)^3*ln(-b+_a)*b^3*a-3/(b-c)^3/(a-b)^3*ln(-b+_a)*b^2*c*a+1/(b-c)^3/(a-b)^3*ln(-b+_a)*b^4+1/(b-c)^3/(a-b)^3*ln(-b+_a)*b^3*c+3/(b-c)^3/(a-c)^3*ln(-c+_a)*c^2*a*b-1/(b-c)^3/(a-c)^3*ln(-c+_a)*c^3*a-1/(b-c)^3/(a-c)^3*ln(-c+_a)*c^3*b-1/(b-c)^3/(a-c)^3*ln(-c+_a)*c^4-b^3/(b-c)^2/(a-b)^2/(-b+_a))-2*_a^2*a^2*a3*(-a^3/(a-c)^2/(a-b)^2/(-a+_a)-1/(a-c)^3/(a-b)^3*ln(-a+_a)*a^4-1/(a-c)^3/(a-b)^3*ln(-a+_a)*a^3*b-1/(a-c)^3/(a-b)^3*ln(-a+_a)*a^3*c+3/(a-c)^3/(a-b)^3*ln(-a+_a)*a^2*c*b-c^3/(b-c)^2/(a-c)^2/(-c+_a)+1/(b-c)^3/(a-b)^3*ln(-b+_a)*b^3*a-3/(b-c)^3/(a-b)^3*ln(-b+_a)*b^2*c*a+1/(b-c)^3/(a-b)^3*ln(-b+_a)*b^4+1/(b-c)^3/(a-b)^3*ln(-b+_a)*b^3*c+3/(b-c)^3/(a-c)^3*ln(-c+_a)*c^2*a*b-1/(b-c)^3/(a-c)^3*ln(-c+_a)*c^3*a-1/(b-c)^3/(a-c)^3*ln(-c+_a)*c^3*b-1/(b-c)^3/(a-c)^3*ln(-c+_a)*c^4-b^3/(b-c)^2/(a-b)^2/(-b+_a))-2*_a^2*a1*b^2*(-a^3/(a-c)^2/(a-b)^2/(-a+_a)-1/(a-c)^3/(a-b)^3*ln(-a+_a)*a^4-1/(a-c)^3/(a-b)^3*ln(-a+_a)*a^3*b-1/(a-c)^3/(a-b)^3*ln(-a+_a)*a^3*c+3/(a-c)^3/(a-b)^3*ln(-a+_a)*a^2*c*b-c^3/(b-c)^2/(a-c)^2/(-c+_a)+1/(b-c)^3/(a-b)^3*ln(-b+_a)*b^3*a-3/(b-c)^3/(a-b)^3*ln(-b+_a)*b^2*c*a+1/(b-c)^3/(a-b)^3*ln(-b+_a)*b^4+1/(b-c)^3/(a-b)^3*ln(-b+_a)*b^3*c+3/(b-c)^3/(a-c)^3*ln(-c+_a)*c^2*a*b-1/(b-c)^3/(a-c)^3*ln(-c+_a)*c^3*a-1/(b-c)^3/(a-c)^3*ln(-c+_a)*c^3*b-1/(b-c)^3/(a-c)^3*ln(-c+_a)*c^4-b^3/(b-c)^2/(a-b)^2/(-b+_a))-2*_a^2*a1*c^2*(-a^3/(a-c)^2/(a-b)^2/(-a+_a)-1/(a-c)^3/(a-b)^3*ln(-a+_a)*a^4-1/(a-c)^3/(a-b)^3*ln(-a+_a)*a^3*b-1/(a-c)^3/(a-b)^3*ln(-a+_a)*a^3*c+3/(a-c)^3/(a-b)^3*ln(-a+_a)*a^2*c*b-c^3/(b-c)^2/(a-c)^2/(-c+_a)+1/(b-c)^3/(a-b)^3*ln(-b+_a)*b^3*a-3/(b-c)^3/(a-b)^3*ln(-b+_a)*b^2*c*a+1/(b-c)^3/(a-b)^3*ln(-b+_a)*b^4+1/(b-c)^3/(a-b)^3*ln(-b+_a)*b^3*c+3/(b-c)^3/(a-c)^3*ln(-c+_a)*c^2*a*b-1/(b-c)^3/(a-c)^3*ln(-c+_a)*c^3*a-1/(b-c)^3/(a-c)^3*ln(-c+_a)*c^3*b-1/(b-c)^3/(a-c)^3*ln(-c+_a)*c^4-b^3/(b-c)^2/(a-b)^2/(-b+_a))-4*_a^2*a2*c^2*(-a^3/(a-c)^2/(a-b)^2/(-a+_a)-1/(a-c)^3/(a-b)^3*ln(-a+_a)*a^4-1/(a-c)^3/(a-b)^3*ln(-a+_a)*a^3*b-1/(a-c)^3/(a-b)^3*ln(-a+_a)*a^3*c+3/(a-c)^3/(a-b)^3*ln(-a+_a)*a^2*c*b-c^3/(b-c)^2/(a-c)^2/(-c+_a)+1/(b-c)^3/(a-b)^3*ln(-b+_a)*b^3*a-3/(b-c)^3/(a-b)^3*ln(-b+_a)*b^2*c*a+1/(b-c)^3/(a-b)^3*ln(-b+_a)*b^4+1/(b-c)^3/(a-b)^3*ln(-b+_a)*b^3*c+3/(b-c)^3/(a-c)^3*ln(-c+_a)*c^2*a*b-1/(b-c)^3/(a-c)^3*ln(-c+_a)*c^3*a-1/(b-c)^3/(a-c)^3*ln(-c+_a)*c^3*b-1/(b-c)^3/(a-c)^3*ln(-c+_a)*c^4-b^3/(b-c)^2/(a-b)^2/(-b+_a))-2*_a^2*a3*b^2*(-a^3/(a-c)^2/(a-b)^2/(-a+_a)-1/(a-c)^3/(a-b)^3*ln(-a+_a)*a^4-1/(a-c)^3/(a-b)^3*ln(-a+_a)*a^3*b-1/(a-c)^3/(a-b)^3*ln(-a+_a)*a^3*c+3/(a-c)^3/(a-b)^3*ln(-a+_a)*a^2*c*b-c^3/(b-c)^2/(a-c)^2/(-c+_a)+1/(b-c)^3/(a-b)^3*ln(-b+_a)*b^3*a-3/(b-c)^3/(a-b)^3*ln(-b+_a)*b^2*c*a+1/(b-c)^3/(a-b)^3*ln(-b+_a)*b^4+1/(b-c)^3/(a-b)^3*ln(-b+_a)*b^3*c+3/(b-c)^3/(a-c)^3*ln(-c+_a)*c^2*a*b-1/(b-c)^3/(a-c)^3*ln(-c+_a)*c^3*a-1/(b-c)^3/(a-c)^3*ln(-c+_a)*c^3*b-1/(b-c)^3/(a-c)^3*ln(-c+_a)*c^4-b^3/(b-c)^2/(a-b)^2/(-b+_a))-_a^3*a^2*a0*(-a^4/(a-c)^2/(a-b)^2/(-a+_a)-2*a^4/(a-c)^3/(a-b)^3*ln(-a+_a)*b-2*a^4/(a-c)^3/(a-b)^3*ln(-a+_a)*c+4*a^3/(a-c)^3/(a-b)^3*ln(-a+_a)*c*b-c^4/(b-c)^2/(a-c)^2/(-c+_a)+2*b^4/(b-c)^3/(a-b)^3*ln(-b+_a)*a-4*b^3/(b-c)^3/(a-b)^3*ln(-b+_a)*c*a+2*b^4/(b-c)^3/(a-b)^3*ln(-b+_a)*c+4*c^3/(b-c)^3/(a-c)^3*ln(-c+_a)*a*b-2*c^4/(b-c)^3/(a-c)^3*ln(-c+_a)*a-2*c^4/(b-c)^3/(a-c)^3*ln(-c+_a)*b-b^4/(b-c)^2/(a-b)^2/(-b+_a))-_a^3*a0*b^2*(-a^4/(a-c)^2/(a-b)^2/(-a+_a)-2*a^4/(a-c)^3/(a-b)^3*ln(-a+_a)*b-2*a^4/(a-c)^3/(a-b)^3*ln(-a+_a)*c+4*a^3/(a-c)^3/(a-b)^3*ln(-a+_a)*c*b-c^4/(b-c)^2/(a-c)^2/(-c+_a)+2*b^4/(b-c)^3/(a-b)^3*ln(-b+_a)*a-4*b^3/(b-c)^3/(a-b)^3*ln(-b+_a)*c*a+2*b^4/(b-c)^3/(a-b)^3*ln(-b+_a)*c+4*c^3/(b-c)^3/(a-c)^3*ln(-c+_a)*a*b-2*c^4/(b-c)^3/(a-c)^3*ln(-c+_a)*a-2*c^4/(b-c)^3/(a-c)^3*ln(-c+_a)*b-b^4/(b-c)^2/(a-b)^2/(-b+_a))-_a^3*a0*c^2*(-a^4/(a-c)^2/(a-b)^2/(-a+_a)-2*a^4/(a-c)^3/(a-b)^3*ln(-a+_a)*b-2*a^4/(a-c)^3/(a-b)^3*ln(-a+_a)*c+4*a^3/(a-c)^3/(a-b)^3*ln(-a+_a)*c*b-c^4/(b-c)^2/(a-c)^2/(-c+_a)+2*b^4/(b-c)^3/(a-b)^3*ln(-b+_a)*a-4*b^3/(b-c)^3/(a-b)^3*ln(-b+_a)*c*a+2*b^4/(b-c)^3/(a-b)^3*ln(-b+_a)*c+4*c^3/(b-c)^3/(a-c)^3*ln(-c+_a)*a*b-2*c^4/(b-c)^3/(a-c)^3*ln(-c+_a)*a-2*c^4/(b-c)^3/(a-c)^3*ln(-c+_a)*b-b^4/(b-c)^2/(a-b)^2/(-b+_a))+_a^2*a^3*a0*(-a^4/(a-c)^2/(a-b)^2/(-a+_a)-2*a^4/(a-c)^3/(a-b)^3*ln(-a+_a)*b-2*a^4/(a-c)^3/(a-b)^3*ln(-a+_a)*c+4*a^3/(a-c)^3/(a-b)^3*ln(-a+_a)*c*b-c^4/(b-c)^2/(a-c)^2/(-c+_a)+2*b^4/(b-c)^3/(a-b)^3*ln(-b+_a)*a-4*b^3/(b-c)^3/(a-b)^3*ln(-b+_a)*c*a+2*b^4/(b-c)^3/(a-b)^3*ln(-b+_a)*c+4*c^3/(b-c)^3/(a-c)^3*ln(-c+_a)*a*b-2*c^4/(b-c)^3/(a-c)^3*ln(-c+_a)*a-2*c^4/(b-c)^3/(a-c)^3*ln(-c+_a)*b-b^4/(b-c)^2/(a-b)^2/(-b+_a))+_a^2*a0*b^3*(-a^4/(a-c)^2/(a-b)^2/(-a+_a)-2*a^4/(a-c)^3/(a-b)^3*ln(-a+_a)*b-2*a^4/(a-c)^3/(a-b)^3*ln(-a+_a)*c+4*a^3/(a-c)^3/(a-b)^3*ln(-a+_a)*c*b-c^4/(b-c)^2/(a-c)^2/(-c+_a)+2*b^4/(b-c)^3/(a-b)^3*ln(-b+_a)*a-4*b^3/(b-c)^3/(a-b)^3*ln(-b+_a)*c*a+2*b^4/(b-c)^3/(a-b)^3*ln(-b+_a)*c+4*c^3/(b-c)^3/(a-c)^3*ln(-c+_a)*a*b-2*c^4/(b-c)^3/(a-c)^3*ln(-c+_a)*a-2*c^4/(b-c)^3/(a-c)^3*ln(-c+_a)*b-b^4/(b-c)^2/(a-b)^2/(-b+_a))+_a^2*a0*c^3*(-a^4/(a-c)^2/(a-b)^2/(-a+_a)-2*a^4/(a-c)^3/(a-b)^3*ln(-a+_a)*b-2*a^4/(a-c)^3/(a-b)^3*ln(-a+_a)*c+4*a^3/(a-c)^3/(a-b)^3*ln(-a+_a)*c*b-c^4/(b-c)^2/(a-c)^2/(-c+_a)+2*b^4/(b-c)^3/(a-b)^3*ln(-b+_a)*a-4*b^3/(b-c)^3/(a-b)^3*ln(-b+_a)*c*a+2*b^4/(b-c)^3/(a-b)^3*ln(-b+_a)*c+4*c^3/(b-c)^3/(a-c)^3*ln(-c+_a)*a*b-2*c^4/(b-c)^3/(a-c)^3*ln(-c+_a)*a-2*c^4/(b-c)^3/(a-c)^3*ln(-c+_a)*b-b^4/(b-c)^2/(a-b)^2/(-b+_a))+_a^2*a*a1*(-a^4/(a-c)^2/(a-b)^2/(-a+_a)-2*a^4/(a-c)^3/(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*(-1/(a-c)^2/(a-b)^2/(-a+_a)-4/(a-c)^3/(a-b)^3*ln(-a+_a)*a+2/(a-c)^3/(a-b)^3*ln(-a+_a)*c+2/(a-c)^3/(a-b)^3*ln(-a+_a)*b-1/(b-c)^2/(a-c)^2/(-c+_a)+4/(b-c)^3/(a-b)^3*ln(-b+_a)*b-2/(b-c)^3/(a-b)^3*ln(-b+_a)*c-2/(b-c)^3/(a-b)^3*ln(-b+_a)*a+2/(b-c)^3/(a-c)^3*ln(-c+_a)*b-4/(b-c)^3/(a-c)^3*ln(-c+_a)*c+2/(b-c)^3/(a-c)^3*ln(-c+_a)*a-1/(b-c)^2/(a-b)^2/(-b+_a))-_a*a^3*a0*b^3*c^2*(-1/(a-c)^2/(a-b)^2/(-a+_a)-4/(a-c)^3/(a-b)^3*ln(-a+_a)*a+2/(a-c)^3/(a-b)^3*ln(-a+_a)*c+2/(a-c)^3/(a-b)^3*ln(-a+_a)*b-1/(b-c)^2/(a-c)^2/(-c+_a)+4/(b-c)^3/(a-b)^3*ln(-b+_a)*b-2/(b-c)^3/(a-b)^3*ln(-b+_a)*c-2/(b-c)^3/(a-b)^3*ln(-b+_a)*a+2/(b-c)^3/(a-c)^3*ln(-c+_a)*b-4/(b-c)^3/(a-c)^3*ln(-c+_a)*c+2/(b-c)^3/(a-c)^3*ln(-c+_a)*a-1/(b-c)^2/(a-b)^2/(-b+_a))-_a*a^3*a0*b^2*c^3*(-1/(a-c)^2/(a-b)^2/(-a+_a)-4/(a-c)^3/(a-b)^3*ln(-a+_a)*a+2/(a-c)^3/(a-b)^3*ln(-a+_a)*c+2/(a-c)^3/(a-b)^3*ln(-a+_a)*b-1/(b-c)^2/(a-c)^2/(-c+_a)+4/(b-c)^3/(a-b)^3*ln(-b+_a)*b-2/(b-c)^3/(a-b)^3*ln(-b+_a)*c-2/(b-c)^3/(a-b)^3*ln(-b+_a)*a+2/(b-c)^3/(a-c)^3*ln(-c+_a)*b-4/(b-c)^3/(a-c)^3*ln(-c+_a)*c+2/(b-c)^3/(a-c)^3*ln(-c+_a)*a-1/(b-c)^2/(a-b)^2/(-b+_a))-_a*a^2*a0*b^3*c^3*(-1/(a-c)^2/(a-b)^2/(-a+_a)-4/(a-c)^3/(a-b)^3*ln(-a+_a)*a+2/(a-c)^3/(a-b)^3*ln(-a+_a)*c+2/(a-c)^3/(a-b)^3*ln(-a+_a)*b-1/(b-c)^2/(a-c)^2/(-c+_a)+4/(b-c)^3/(a-b)^3*ln(-b+_a)*b-2/(b-c)^3/(a-b)^3*ln(-b+_a)*c-2/(b-c)^3/(a-b)^3*ln(-b+_a)*a+2/(b-c)^3/(a-c)^3*ln(-c+_a)*b-4/(b-c)^3/(a-c)^3*ln(-c+_a)*c+2/(b-c)^3/(a-c)^3*ln(-c+_a)*a-1/(b-c)^2/(a-b)^2/(-b+_a))+2*_a^2*a^2*a2*b*c^2*(-1/(a-c)^2/(a-b)^2/(-a+_a)-4/(a-c)^3/(a-b)^3*ln(-a+_a)*a+2/(a-c)^3/(a-b)^3*ln(-a+_a)*c+2/(a-c)^3/(a-b)^3*ln(-a+_a)*b-1/(b-c)^2/(a-c)^2/(-c+_a)+4/(b-c)^3/(a-b)^3*ln(-b+_a)*b-2/(b-c)^3/(a-b)^3*ln(-b+_a)*c-2/(b-c)^3/(a-b)^3*ln(-b+_a)*a+2/(b-c)^3/(a-c)^3*ln(-c+_a)*b-4/(b-c)^3/(a-c)^3*ln(-c+_a)*c+2/(b-c)^3/(a-c)^3*ln(-c+_a)*a-1/(b-c)^2/(a-b)^2/(-b+_a))+_a^2*a^2*a3*b^2*c*(-1/(a-c)^2/(a-b)^2/(-a+_a)-4/(a-c)^3/(a-b)^3*ln(-a+_a)*a+2/(a-c)^3/(a-b)^3*ln(-a+_a)*c+2/(a-c)^3/(a-b)^3*ln(-a+_a)*b-1/(b-c)^2/(a-c)^2/(-c+_a)+4/(b-c)^3/(a-b)^3*ln(-b+_a)*b-2/(b-c)^3/(a-b)^3*ln(-b+_a)*c-2/(b-c)^3/(a-b)^3*ln(-b+_a)*a+2/(b-c)^3/(a-c)^3*ln(-c+_a)*b-4/(b-c)^3/(a-c)^3*ln(-c+_a)*c+2/(b-c)^3/(a-c)^3*ln(-c+_a)*a-1/(b-c)^2/(a-b)^2/(-b+_a))+_a^2*a*a1*b^2*c^2*(-1/(a-c)^2/(a-b)^2/(-a+_a)-4/(a-c)^3/(a-b)^3*ln(-a+_a)*a+2/(a-c)^3/(a-b)^3*ln(-a+_a)*c+2/(a-c)^3/(a-b)^3*ln(-a+_a)*b-1/(b-c)^2/(a-c)^2/(-c+_a)+4/(b-c)^3/(a-b)^3*ln(-b+_a)*b-2/(b-c)^3/(a-b)^3*ln(-b+_a)*c-2/(b-c)^3/(a-b)^3*ln(-b+_a)*a+2/(b-c)^3/(a-c)^3*ln(-c+_a)*b-4/(b-c)^3/(a-c)^3*ln(-c+_a)*c+2/(b-c)^3/(a-c)^3*ln(-c+_a)*a-1/(b-c)^2/(a-b)^2/(-b+_a))-2*_a*a^3*a2*b*c^2*(-1/(a-c)^2/(a-b)^2/(-a+_a)-4/(a-c)^3/(a-b)^3*ln(-a+_a)*a+2/(a-c)^3/(a-b)^3*ln(-a+_a)*c+2/(a-c)^3/(a-b)^3*ln(-a+_a)*b-1/(b-c)^2/(a-c)^2/(-c+_a)+4/(b-c)^3/(a-b)^3*ln(-b+_a)*b-2/(b-c)^3/(a-b)^3*ln(-b+_a)*c-2/(b-c)^3/(a-b)^3*ln(-b+_a)*a+2/(b-c)^3/(a-c)^3*ln(-c+_a)*b-4/(b-c)^3/(a-c)^3*ln(-c+_a)*c+2/(b-c)^3/(a-c)^3*ln(-c+_a)*a-1/(b-c)^2/(a-b)^2/(-b+_a))-_a*a^3*a3*b^2*c*(-1/(a-c)^2/(a-b)^2/(-a+_a)-4/(a-c)^3/(a-b)^3*ln(-a+_a)*a+2/(a-c)^3/(a-b)^3*ln(-a+_a)*c+2/(a-c)^3/(a-b)^3*ln(-a+_a)*b-1/(b-c)^2/(a-c)^2/(-c+_a)+4/(b-c)^3/(a-b)^3*ln(-b+_a)*b-2/(b-c)^3/(a-b)^3*ln(-b+_a)*c-2/(b-c)^3/(a-b)^3*ln(-b+_a)*a+2/(b-c)^3/(a-c)^3*ln(-c+_a)*b-4/(b-c)^3/(a-c)^3*ln(-c+_a)*c+2/(b-c)^3/(a-c)^3*ln(-c+_a)*a-1/(b-c)^2/(a-b)^2/(-b+_a))-2*_a*a^2*a2*b*c^3*(-1/(a-c)^2/(a-b)^2/(-a+_a)-4/(a-c)^3/(a-b)^3*ln(-a+_a)*a+2/(a-c)^3/(a-b)^3*ln(-a+_a)*c+2/(a-c)^3/(a-b)^3*ln(-a+_a)*b-1/(b-c)^2/(a-c)^2/(-c+_a)+4/(b-c)^3/(a-b)^3*ln(-b+_a)*b-2/(b-c)^3/(a-b)^3*ln(-b+_a)*c-2/(b-c)^3/(a-b)^3*ln(-b+_a)*a+2/(b-c)^3/(a-c)^3*ln(-c+_a)*b-4/(b-c)^3/(a-c)^3*ln(-c+_a)*c+2/(b-c)^3/(a-c)^3*ln(-c+_a)*a-1/(b-c)^2/(a-b)^2/(-b+_a))-_a*a^2*a3*b^3*c*(-1/(a-c)^2/(a-b)^2/(-a+_a)-4/(a-c)^3/(a-b)^3*ln(-a+_a)*a+2/(a-c)^3/(a-b)^3*ln(-a+_a)*c+2/(a-c)^3/(a-b)^3*ln(-a+_a)*b-1/(b-c)^2/(a-c)^2/(-c+_a)+4/(b-c)^3/(a-b)^3*ln(-b+_a)*b-2/(b-c)^3/(a-b)^3*ln(-b+_a)*c-2/(b-c)^3/(a-b)^3*ln(-b+_a)*a+2/(b-c)^3/(a-c)^3*ln(-c+_a)*b-4/(b-c)^3/(a-c)^3*ln(-c+_a)*c+2/(b-c)^3/(a-c)^3*ln(-c+_a)*a-1/(b-c)^2/(a-b)^2/(-b+_a))-_a*a*a1*b^3*c^2*(-1/(a-c)^2/(a-b)^2/(-a+_a)-4/(a-c)^3/(a-b)^3*ln(-a+_a)*a+2/(a-c)^3/(a-b)^3*ln(-a+_a)*c+2/(a-c)^3/(a-b)^3*ln(-a+_a)*b-1/(b-c)^2/(a-c)^2/(-c+_a)+4/(b-c)^3/(a-b)^3*ln(-b+_a)*b-2/(b-c)^3/(a-b)^3*ln(-b+_a)*c-2/(b-c)^3/(a-b)^3*ln(-b+_a)*a+2/(b-c)^3/(a-c)^3*ln(-c+_a)*b-4/(b-c)^3/(a-c)^3*ln(-c+_a)*c+2/(b-c)^3/(a-c)^3*ln(-c+_a)*a-1/(b-c)^2/(a-b)^2/(-b+_a))-_a*a*a1*b^2*c^3*(-1/(a-c)^2/(a-b)^2/(-a+_a)-4/(a-c)^3/(a-b)^3*ln(-a+_a)*a+2/(a-c)^3/(a-b)^3*ln(-a+_a)*c+2/(a-c)^3/(a-b)^3*ln(-a+_a)*b-1/(b-c)^2/(a-c)^2/(-c+_a)+4/(b-c)^3/(a-b)^3*ln(-b+_a)*b-2/(b-c)^3/(a-b)^3*ln(-b+_a)*c-2/(b-c)^3/(a-b)^3*ln(-b+_a)*a+2/(b-c)^3/(a-c)^3*ln(-c+_a)*b-4/(b-c)^3/(a-c)^3*ln(-c+_a)*c+2/(b-c)^3/(a-c)^3*ln(-c+_a)*a-1/(b-c)^2/(a-b)^2/(-b+_a))-_a^3*a^2*a0*b^2*c^2*(-1/(a-c)^2/(a-b)^2/(-a+_a)-4/(a-c)^3/(a-b)^3*ln(-a+_a)*a+2/(a-c)^3/(a-b)^3*ln(-a+_a)*c+2/(a-c)^3/(a-b)^3*ln(-a+_a)*b-1/(b-c)^2/(a-c)^2/(-c+_a)+4/(b-c)^3/(a-b)^3*ln(-b+_a)*b-2/(b-c)^3/(a-b)^3*ln(-b+_a)*c-2/(b-c)^3/(a-b)^3*ln(-b+_a)*a+2/(b-c)^3/(a-c)^3*ln(-c+_a)*b-4/(b-c)^3/(a-c)^3*ln(-c+_a)*c+2/(b-c)^3/(a-c)^3*ln(-c+_a)*a-1/(b-c)^2/(a-b)^2/(-b+_a))+_a^2*a^3*a0*b^2*c^2*(-1/(a-c)^2/(a-b)^2/(-a+_a)-4/(a-c)^3/(a-b)^3*ln(-a+_a)*a+2/(a-c)^3/(a-b)^3*ln(-a+_a)*c+2/(a-c)^3/(a-b)^3*ln(-a+_a)*b-1/(b-c)^2/(a-c)^2/(-c+_a)+4/(b-c)^3/(a-b)^3*ln(-b+_a)*b-2/(b-c)^3/(a-b)^3*ln(-b+_a)*c-2/(b-c)^3/(a-b)^3*ln(-b+_a)*a+2/(b-c)^3/(a-c)^3*ln(-c+_a)*b-4/(b-c)^3/(a-c)^3*ln(-c+_a)*c+2/(b-c)^3/(a-c)^3*ln(-c+_a)*a-1/(b-c)^2/(a-b)^2/(-b+_a))+_a^2*a^2*a0*b^3*c^2*(-1/(a-c)^2/(a-b)^2/(-a+_a)-4/(a-c)^3/(a-b)^3*ln(-a+_a)*a+2/(a-c)^3/(a-b)^3*ln(-a+_a)*c+2/(a-c)^3/(a-b)^3*ln(-a+_a)*b-1/(b-c)^2/(a-c)^2/(-c+_a)+4/(b-c)^3/(a-b)^3*ln(-b+_a)*b-2/(b-c)^3/(a-b)^3*ln(-b+_a)*c-2/(b-c)^3/(a-b)^3*ln(-b+_a)*a+2/(b-c)^3/(a-c)^3*ln(-c+_a)*b-4/(b-c)^3/(a-c)^3*ln(-c+_a)*c+2/(b-c)^3/(a-c)^3*ln(-c+_a)*a-1/(b-c)^2/(a-b)^2/(-b+_a))+2*_a^3*a^2*a0*b^2*c*(-a/(a-c)^2/(a-b)^2/(-a+_a)-3/(a-c)^3/(a-b)^3*ln(-a+_a)*a^2+1/(a-c)^3/(a-b)^3*ln(-a+_a)*a*b+1/(a-c)^3/(a-b)^3*ln(-a+_a)*c*a+1/(a-c)^3/(a-b)^3*ln(-a+_a)*c*b-c/(b-c)^2/(a-c)^2/(-c+_a)-1/(b-c)^3/(a-b)^3*ln(-b+_a)*a*b-1/(b-c)^3/(a-b)^3*ln(-b+_a)*c*a+3/(b-c)^3/(a-b)^3*ln(-b+_a)*b^2-1/(b-c)^3/(a-b)^3*ln(-b+_a)*c*b+1/(b-c)^3/(a-c)^3*ln(-c+_a)*a*b+1/(b-c)^3/(a-c)^3*ln(-c+_a)*c*a+1/(b-c)^3/(a-c)^3*ln(-c+_a)*c*b-3/(b-c)^3/(a-c)^3*ln(-c+_a)*c^2-b/(b-c)^2/(a-b)^2/(-b+_a))+2*_a^3*a^2*a0*b*c^2*(-a/(a-c)^2/(a-b)^2/(-a+_a)-3/(a-c)^3/(a-b)^3*ln(-a+_a)*a^2+1/(a-c)^3/(a-b)^3*ln(-a+_a)*a*b+1/(a-c)^3/(a-b)^3*ln(-a+_a)*c*a+1/(a-c)^3/(a-b)^3*ln(-a+_a)*c*b-c/(b-c)^2/(a-c)^2/(-c+_a)-1/(b-c)^3/(a-b)^3*ln(-b+_a)*a*b-1/(b-c)^3/(a-b)^3*ln(-b+_a)*c*a+3/(b-c)^3/(a-b)^3*ln(-b+_a)*b^2-1/(b-c)^3/(a-b)^3*ln(-b+_a)*c*b+1/(b-c)^3/(a-c)^3*ln(-c+_a)*a*b+1/(b-c)^3/(a-c)^3*ln(-c+_a)*c*a+1/(b-c)^3/(a-c)^3*ln(-c+_a)*c*b-3/(b-c)^3/(a-c)^3*ln(-c+_a)*c^2-b/(b-c)^2/(a-b)^2/(-b+_a))+2*_a^3*a*a0*b^2*c^2*(-a/(a-c)^2/(a-b)^2/(-a+_a)-3/(a-c)^3/(a-b)^3*ln(-a+_a)*a^2+1/(a-c)^3/(a-b)^3*ln(-a+_a)*a*b+1/(a-c)^3/(a-b)^3*ln(-a+_a)*c*a+1/(a-c)^3/(a-b)^3*ln(-a+_a)*c*b-c/(b-c)^2/(a-c)^2/(-c+_a)-1/(b-c)^3/(a-b)^3*ln(-b+_a)*a*b-1/(b-c)^3/(a-b)^3*ln(-b+_a)*c*a+3/(b-c)^3/(a-b)^3*ln(-b+_a)*b^2-1/(b-c)^3/(a-b)^3*ln(-b+_a)*c*b+1/(b-c)^3/(a-c)^3*ln(-c+_a)*a*b+1/(b-c)^3/(a-c)^3*ln(-c+_a)*c*a+1/(b-c)^3/(a-c)^3*ln(-c+_a)*c*b-3/(b-c)^3/(a-c)^3*ln(-c+_a)*c^2-b/(b-c)^2/(a-b)^2/(-b+_a))-2*_a^2*a^3*a0*b^2*c*(-a/(a-c)^2/(a-b)^2/(-a+_a)-3/(a-c)^3/(a-b)^3*ln(-a+_a)*a^2+1/(a-c)^3/(a-b)^3*ln(-a+_a)*a*b+1/(a-c)^3/(a-b)^3*ln(-a+_a)*c*a+1/(a-c)^3/(a-b)^3*ln(-a+_a)*c*b-c/(b-c)^2/(a-c)^2/(-c+_a)-1/(b-c)^3/(a-b)^3*ln(-b+_a)*a*b-1/(b-c)^3/(a-b)^3*ln(-b+_a)*c*a+3/(b-c)^3/(a-b)^3*ln(-b+_a)*b^2-1/(b-c)^3/(a-b)^3*ln(-b+_a)*c*b+1/(b-c)^3/(a-c)^3*ln(-c+_a)*a*b+1/(b-c)^3/(a-c)^3*ln(-c+_a)*c*a+1/(b-c)^3/(a-c)^3*ln(-c+_a)*c*b-3/(b-c)^3/(a-c)^3*ln(-c+_a)*c^2-b/(b-c)^2/(a-b)^2/(-b+_a))-2*_a^2*a^3*a0*b*c^2*(-a/(a-c)^2/(a-b)^2/(-a+_a)-3/(a-c)^3/(a-b)^3*ln(-a+_a)*a^2+1/(a-c)^3/(a-b)^3*ln(-a+_a)*a*b+1/(a-c)^3/(a-b)^3*ln(-a+_a)*c*a+1/(a-c)^3/(a-b)^3*ln(-a+_a)*c*b-c/(b-c)^2/(a-c)^2/(-c+_a)-1/(b-c)^3/(a-b)^3*ln(-b+_a)*a*b-1/(b-c)^3/(a-b)^3*ln(-b+_a)*c*a+3/(b-c)^3/(a-b)^3*ln(-b+_a)*b^2-1/(b-c)^3/(a-b)^3*ln(-b+_a)*c*b+1/(b-c)^3/(a-c)^3*ln(-c+_a)*a*b+1/(b-c)^3/(a-c)^3*ln(-c+_a)*c*a+1/(b-c)^3/(a-c)^3*ln(-c+_a)*c*b-3/(b-c)^3/(a-c)^3*ln(-c+_a)*c^2-b/(b-c)^2/(a-b)^2/(-b+_a))-2*_a^2*a^2*a0*b^3*c*(-a/(a-c)^2/(a-b)^2/(-a+_a)-3/(a-c)^3/(a-b)^3*ln(-a+_a)*a^2+1/(a-c)^3/(a-b)^3*ln(-a+_a)*a*b+1/(a-c)^3/(a-b)^3*ln(-a+_a)*c*a+1/(a-c)^3/(a-b)^3*ln(-a+_a)*c*b-c/(b-c)^2/(a-c)^2/(-c+_a)-1/(b-c)^3/(a-b)^3*ln(-b+_a)*a*b-1/(b-c)^3/(a-b)^3*ln(-b+_a)*c*a+3/(b-c)^3/(a-b)^3*ln(-b+_a)*b^2-1/(b-c)^3/(a-b)^3*ln(-b+_a)*c*b+1/(b-c)^3/(a-c)^3*ln(-c+_a)*a*b+1/(b-c)^3/(a-c)^3*ln(-c+_a)*c*a+1/(b-c)^3/(a-c)^3*ln(-c+_a)*c*b-3/(b-c)^3/(a-c)^3*ln(-c+_a)*c^2-b/(b-c)^2/(a-b)^2/(-b+_a))-6*_a^2*a^2*a0*b^2*c^2*(-a/(a-c)^2/(a-b)^2/(-a+_a)-3/(a-c)^3/(a-b)^3*ln(-a+_a)*a^2+1/(a-c)^3/(a-b)^3*ln(-a+_a)*a*b+1/(a-c)^3/(a-b)^3*ln(-a+_a)*c*a+1/(a-c)^3/(a-b)^3*ln(-a+_a)*c*b-c/(b-c)^2/(a-c)^2/(-c+_a)-1/(b-c)^3/(a-b)^3*ln(-b+_a)*a*b-1/(b-c)^3/(a-b)^3*ln(-b+_a)*c*a+3/(b-c)^3/(a-b)^3*ln(-b+_a)*b^2-1/(b-c)^3/(a-b)^3*ln(-b+_a)*c*b+1/(b-c)^3/(a-c)^3*ln(-c+_a)*a*b+1/(b-c)^3/(a-c)^3*ln(-c+_a)*c*a+1/(b-c)^3/(a-c)^3*ln(-c+_a)*c*b-3/(b-c)^3/(a-c)^3*ln(-c+_a)*c^2-b/(b-c)^2/(a-b)^2/(-b+_a))-2*_a^2*a^2*a0*b*c^3*(-a/(a-c)^2/(a-b)^2/(-a+_a)-3/(a-c)^3/(a-b)^3*ln(-a+_a)*a^2+1/(a-c)^3/(a-b)^3*ln(-a+_a)*a*b+1/(a-c)^3/(a-b)^3*ln(-a+_a)*c*a+1/(a-c)^3/(a-b)^3*ln(-a+_a)*c*b-c/(b-c)^2/(a-c)^2/(-c+_a)-1/(b-c)^3/(a-b)^3*ln(-b+_a)*a*b-1/(b-c)^3/(a-b)^3*ln(-b+_a)*c*a+3/(b-c)^3/(a-b)^3*ln(-b+_a)*b^2-1/(b-c)^3/(a-b)^3*ln(-b+_a)*c*b+1/(b-c)^3/(a-c)^3*ln(-c+_a)*a*b+1/(b-c)^3/(a-c)^3*ln(-c+_a)*c*a+1/(b-c)^3/(a-c)^3*ln(-c+_a)*c*b-3/(b-c)^3/(a-c)^3*ln(-c+_a)*c^2-b/(b-c)^2/(a-b)^2/(-b+_a))-2*_a^2*a*a0*b^3*c^2*(-a/(a-c)^2/(a-b)^2/(-a+_a)-3/(a-c)^3/(a-b)^3*ln(-a+_a)*a^2+1/(a-c)^3/(a-b)^3*ln(-a+_a)*a*b+1/(a-c)^3/(a-b)^3*ln(-a+_a)*c*a+1/(a-c)^3/(a-b)^3*ln(-a+_a)*c*b-c/(b-c)^2/(a-c)^2/(-c+_a)-1/(b-c)^3/(a-b)^3*ln(-b+_a)*a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(a-b)^3*ln(-a+_a)*a*b+1/(a-c)^3/(a-b)^3*ln(-a+_a)*c*a+1/(a-c)^3/(a-b)^3*ln(-a+_a)*c*b-c/(b-c)^2/(a-c)^2/(-c+_a)-1/(b-c)^3/(a-b)^3*ln(-b+_a)*a*b-1/(b-c)^3/(a-b)^3*ln(-b+_a)*c*a+3/(b-c)^3/(a-b)^3*ln(-b+_a)*b^2-1/(b-c)^3/(a-b)^3*ln(-b+_a)*c*b+1/(b-c)^3/(a-c)^3*ln(-c+_a)*a*b+1/(b-c)^3/(a-c)^3*ln(-c+_a)*c*a+1/(b-c)^3/(a-c)^3*ln(-c+_a)*c*b-3/(b-c)^3/(a-c)^3*ln(-c+_a)*c^2-b/(b-c)^2/(a-b)^2/(-b+_a))+2*_a*a*a3*b^3*c*(-a/(a-c)^2/(a-b)^2/(-a+_a)-3/(a-c)^3/(a-b)^3*ln(-a+_a)*a^2+1/(a-c)^3/(a-b)^3*ln(-a+_a)*a*b+1/(a-c)^3/(a-b)^3*ln(-a+_a)*c*a+1/(a-c)^3/(a-b)^3*ln(-a+_a)*c*b-c/(b-c)^2/(a-c)^2/(-c+_a)-1/(b-c)^3/(a-b)^3*ln(-b+_a)*a*b-1/(b-c)^3/(a-b)^3*ln(-b+_a)*c*a+3/(b-c)^3/(a-b)^3*ln(-b+_a)*b^2-1/(b-c)^3/(a-b)^3*ln(-b+_a)*c*b+1/(b-c)^3/(a-c)^3*ln(-c+_a)*a*b+1/(b-c)^3/(a-c)^3*ln(-c+_a)*c*a+1/(b-c)^3/(a-c)^3*ln(-c+_a)*c*b-3/(b-c)^3/(a-c)^3*ln(-c+_a)*c^2-b/(b-c)^2/(a-b)^2/(-b+_a))+_a^2*a*a0*(_a-a^6/(a-c)^2/(a-b)^2/(-a+_a)-b^6/(b-c)^2/(a-b)^2/(-b+_a)+2*a^7/(a-c)^3/(a-b)^3*ln(-a+_a)-4*a^6/(a-c)^3/(a-b)^3*ln(-a+_a)*b-4*a^6/(a-c)^3/(a-b)^3*ln(-a+_a)*c+6*a^5/(a-c)^3/(a-b)^3*ln(-a+_a)*c*b-c^6/(b-c)^2/(a-c)^2/(-c+_a)+4*b^6/(b-c)^3/(a-b)^3*ln(-b+_a)*a-6*b^5/(b-c)^3/(a-b)^3*ln(-b+_a)*c*a-2*b^7/(b-c)^3/(a-b)^3*ln(-b+_a)+4*b^6/(b-c)^3/(a-b)^3*ln(-b+_a)*c+6*c^5/(b-c)^3/(a-c)^3*ln(-c+_a)*a*b-4*c^6/(b-c)^3/(a-c)^3*ln(-c+_a)*a-4*c^6/(b-c)^3/(a-c)^3*ln(-c+_a)*b+2*c^7/(b-c)^3/(a-c)^3*ln(-c+_a))+_a^2*a0*b*(_a-a^6/(a-c)^2/(a-b)^2/(-a+_a)-b^6/(b-c)^2/(a-b)^2/(-b+_a)+2*a^7/(a-c)^3/(a-b)^3*ln(-a+_a)-4*a^6/(a-c)^3/(a-b)^3*ln(-a+_a)*b-4*a^6/(a-c)^3/(a-b)^3*ln(-a+_a)*c+6*a^5/(a-c)^3/(a-b)^3*ln(-a+_a)*c*b-c^6/(b-c)^2/(a-c)^2/(-c+_a)+4*b^6/(b-c)^3/(a-b)^3*ln(-b+_a)*a-6*b^5/(b-c)^3/(a-b)^3*ln(-b+_a)*c*a-2*b^7/(b-c)^3/(a-b)^3*ln(-b+_a)+4*b^6/(b-c)^3/(a-b)^3*ln(-b+_a)*c+6*c^5/(b-c)^3/(a-c)^3*ln(-c+_a)*a*b-4*c^6/(b-c)^3/(a-c)^3*ln(-c+_a)*a-4*c^6/(b-c)^3/(a-c)^3*ln(-c+_a)*b+2*c^7/(b-c)^3/(a-c)^3*ln(-c+_a))+_a^2*a0*c*(_a-a^6/(a-c)^2/(a-b)^2/(-a+_a)-b^6/(b-c)^2/(a-b)^2/(-b+_a)+2*a^7/(a-c)^3/(a-b)^3*ln(-a+_a)-4*a^6/(a-c)^3/(a-b)^3*ln(-a+_a)*b-4*a^6/(a-c)^3/(a-b)^3*ln(-a+_a)*c+6*a^5/(a-c)^3/(a-b)^3*ln(-a+_a)*c*b-c^6/(b-c)^2/(a-c)^2/(-c+_a)+4*b^6/(b-c)^3/(a-b)^3*ln(-b+_a)*a-6*b^5/(b-c)^3/(a-b)^3*ln(-b+_a)*c*a-2*b^7/(b-c)^3/(a-b)^3*ln(-b+_a)+4*b^6/(b-c)^3/(a-b)^3*ln(-b+_a)*c+6*c^5/(b-c)^3/(a-c)^3*ln(-c+_a)*a*b-4*c^6/(b-c)^3/(a-c)^3*ln(-c+_a)*a-4*c^6/(b-c)^3/(a-c)^3*ln(-c+_a)*b+2*c^7/(b-c)^3/(a-c)^3*ln(-c+_a))-8*_a^2*a*a2*c*(-a^3/(a-c)^2/(a-b)^2/(-a+_a)-1/(a-c)^3/(a-b)^3*ln(-a+_a)*a^4-1/(a-c)^3/(a-b)^3*ln(-a+_a)*a^3*b-1/(a-c)^3/(a-b)^3*ln(-a+_a)*a^3*c+3/(a-c)^3/(a-b)^3*ln(-a+_a)*a^2*c*b-c^3/(b-c)^2/(a-c)^2/(-c+_a)+1/(b-c)^3/(a-b)^3*ln(-b+_a)*b^3*a-3/(b-c)^3/(a-b)^3*ln(-b+_a)*b^2*c*a+1/(b-c)^3/(a-b)^3*ln(-b+_a)*b^4+1/(b-c)^3/(a-b)^3*ln(-b+_a)*b^3*c+3/(b-c)^3/(a-c)^3*ln(-c+_a)*c^2*a*b-1/(b-c)^3/(a-c)^3*ln(-c+_a)*c^3*a-1/(b-c)^3/(a-c)^3*ln(-c+_a)*c^3*b-1/(b-c)^3/(a-c)^3*ln(-c+_a)*c^4-b^3/(b-c)^2/(a-b)^2/(-b+_a))-4*_a^2*a*a3*b*(-a^3/(a-c)^2/(a-b)^2/(-a+_a)-1/(a-c)^3/(a-b)^3*ln(-a+_a)*a^4-1/(a-c)^3/(a-b)^3*ln(-a+_a)*a^3*b-1/(a-c)^3/(a-b)^3*ln(-a+_a)*a^3*c+3/(a-c)^3/(a-b)^3*ln(-a+_a)*a^2*c*b-c^3/(b-c)^2/(a-c)^2/(-c+_a)+1/(b-c)^3/(a-b)^3*ln(-b+_a)*b^3*a-3/(b-c)^3/(a-b)^3*ln(-b+_a)*b^2*c*a+1/(b-c)^3/(a-b)^3*ln(-b+_a)*b^4+1/(b-c)^3/(a-b)^3*ln(-b+_a)*b^3*c+3/(b-c)^3/(a-c)^3*ln(-c+_a)*c^2*a*b-1/(b-c)^3/(a-c)^3*ln(-c+_a)*c^3*a-1/(b-c)^3/(a-c)^3*ln(-c+_a)*c^3*b-1/(b-c)^3/(a-c)^3*ln(-c+_a)*c^4-b^3/(b-c)^2/(a-b)^2/(-b+_a))-2*_a^2*a*a3*c*(-a^3/(a-c)^2/(a-b)^2/(-a+_a)-1/(a-c)^3/(a-b)^3*ln(-a+_a)*a^4-1/(a-c)^3/(a-b)^3*ln(-a+_a)*a^3*b-1/(a-c)^3/(a-b)^3*ln(-a+_a)*a^3*c+3/(a-c)^3/(a-b)^3*ln(-a+_a)*a^2*c*b-c^3/(b-c)^2/(a-c)^2/(-c+_a)+1/(b-c)^3/(a-b)^3*ln(-b+_a)*b^3*a-3/(b-c)^3/(a-b)^3*ln(-b+_a)*b^2*c*a+1/(b-c)^3/(a-b)^3*ln(-b+_a)*b^4+1/(b-c)^3/(a-b)^3*ln(-b+_a)*b^3*c+3/(b-c)^3/(a-c)^3*ln(-c+_a)*c^2*a*b-1/(b-c)^3/(a-c)^3*ln(-c+_a)*c^3*a-1/(b-c)^3/(a-c)^3*ln(-c+_a)*c^3*b-1/(b-c)^3/(a-c)^3*ln(-c+_a)*c^4-b^3/(b-c)^2/(a-b)^2/(-b+_a))-4*_a^2*a1*b*c*(-a^3/(a-c)^2/(a-b)^2/(-a+_a)-1/(a-c)^3/(a-b)^3*ln(-a+_a)*a^4-1/(a-c)^3/(a-b)^3*ln(-a+_a)*a^3*b-1/(a-c)^3/(a-b)^3*ln(-a+_a)*a^3*c+3/(a-c)^3/(a-b)^3*ln(-a+_a)*a^2*c*b-c^3/(b-c)^2/(a-c)^2/(-c+_a)+1/(b-c)^3/(a-b)^3*ln(-b+_a)*b^3*a-3/(b-c)^3/(a-b)^3*ln(-b+_a)*b^2*c*a+1/(b-c)^3/(a-b)^3*ln(-b+_a)*b^4+1/(b-c)^3/(a-b)^3*ln(-b+_a)*b^3*c+3/(b-c)^3/(a-c)^3*ln(-c+_a)*c^2*a*b-1/(b-c)^3/(a-c)^3*ln(-c+_a)*c^3*a-1/(b-c)^3/(a-c)^3*ln(-c+_a)*c^3*b-1/(b-c)^3/(a-c)^3*ln(-c+_a)*c^4-b^3/(b-c)^2/(a-b)^2/(-b+_a))-4*_a^2*a2*b*c*(-a^3/(a-c)^2/(a-b)^2/(-a+_a)-1/(a-c)^3/(a-b)^3*ln(-a+_a)*a^4-1/(a-c)^3/(a-b)^3*ln(-a+_a)*a^3*b-1/(a-c)^3/(a-b)^3*ln(-a+_a)*a^3*c+3/(a-c)^3/(a-b)^3*ln(-a+_a)*a^2*c*b-c^3/(b-c)^2/(a-c)^2/(-c+_a)+1/(b-c)^3/(a-b)^3*ln(-b+_a)*b^3*a-3/(b-c)^3/(a-b)^3*ln(-b+_a)*b^2*c*a+1/(b-c)^3/(a-b)^3*ln(-b+_a)*b^4+1/(b-c)^3/(a-b)^3*ln(-b+_a)*b^3*c+3/(b-c)^3/(a-c)^3*ln(-c+_a)*c^2*a*b-1/(b-c)^3/(a-c)^3*ln(-c+_a)*c^3*a-1/(b-c)^3/(a-c)^3*ln(-c+_a)*c^3*b-1/(b-c)^3/(a-c)^3*ln(-c+_a)*c^4-b^3/(b-c)^2/(a-b)^2/(-b+_a))-2*_a^2*a3*b*c*(-a^3/(a-c)^2/(a-b)^2/(-a+_a)-1/(a-c)^3/(a-b)^3*ln(-a+_a)*a^4-1/(a-c)^3/(a-b)^3*ln(-a+_a)*a^3*b-1/(a-c)^3/(a-b)^3*ln(-a+_a)*a^3*c+3/(a-c)^3/(a-b)^3*ln(-a+_a)*a^2*c*b-c^3/(b-c)^2/(a-c)^2/(-c+_a)+1/(b-c)^3/(a-b)^3*ln(-b+_a)*b^3*a-3/(b-c)^3/(a-b)^3*ln(-b+_a)*b^2*c*a+1/(b-c)^3/(a-b)^3*ln(-b+_a)*b^4+1/(b-c)^3/(a-b)^3*ln(-b+_a)*b^3*c+3/(b-c)^3/(a-c)^3*ln(-c+_a)*c^2*a*b-1/(b-c)^3/(a-c)^3*ln(-c+_a)*c^3*a-1/(b-c)^3/(a-c)^3*ln(-c+_a)*c^3*b-1/(b-c)^3/(a-c)^3*ln(-c+_a)*c^4-b^3/(b-c)^2/(a-b)^2/(-b+_a))+4*_a*a^2*a2*b*(-a^3/(a-c)^2/(a-b)^2/(-a+_a)-1/(a-c)^3/(a-b)^3*ln(-a+_a)*a^4-1/(a-c)^3/(a-b)^3*ln(-a+_a)*a^3*b-1/(a-c)^3/(a-b)^3*ln(-a+_a)*a^3*c+3/(a-c)^3/(a-b)^3*ln(-a+_a)*a^2*c*b-c^3/(b-c)^2/(a-c)^2/(-c+_a)+1/(b-c)^3/(a-b)^3*ln(-b+_a)*b^3*a-3/(b-c)^3/(a-b)^3*ln(-b+_a)*b^2*c*a+1/(b-c)^3/(a-b)^3*ln(-b+_a)*b^4+1/(b-c)^3/(a-b)^3*ln(-b+_a)*b^3*c+3/(b-c)^3/(a-c)^3*ln(-c+_a)*c^2*a*b-1/(b-c)^3/(a-c)^3*ln(-c+_a)*c^3*a-1/(b-c)^3/(a-c)^3*ln(-c+_a)*c^3*b-1/(b-c)^3/(a-c)^3*ln(-c+_a)*c^4-b^3/(b-c)^2/(a-b)^2/(-b+_a))-2*_a^3*a2*(-a^4/(a-c)^2/(a-b)^2/(-a+_a)-2*a^4/(a-c)^3/(a-b)^3*ln(-a+_a)*b-2*a^4/(a-c)^3/(a-b)^3*ln(-a+_a)*c+4*a^3/(a-c)^3/(a-b)^3*ln(-a+_a)*c*b-c^4/(b-c)^2/(a-c)^2/(-c+_a)+2*b^4/(b-c)^3/(a-b)^3*ln(-b+_a)*a-4*b^3/(b-c)^3/(a-b)^3*ln(-b+_a)*c*a+2*b^4/(b-c)^3/(a-b)^3*ln(-b+_a)*c+4*c^3/(b-c)^3/(a-c)^3*ln(-c+_a)*a*b-2*c^4/(b-c)^3/(a-c)^3*ln(-c+_a)*a-2*c^4/(b-c)^3/(a-c)^3*ln(-c+_a)*b-b^4/(b-c)^2/(a-b)^2/(-b+_a))-_a^3*a3*(-a^4/(a-c)^2/(a-b)^2/(-a+_a)-2*a^4/(a-c)^3/(a-b)^3*ln(-a+_a)*b-2*a^4/(a-c)^3/(a-b)^3*ln(-a+_a)*c+4*a^3/(a-c)^3/(a-b)^3*ln(-a+_a)*c*b-c^4/(b-c)^2/(a-c)^2/(-c+_a)+2*b^4/(b-c)^3/(a-b)^3*ln(-b+_a)*a-4*b^3/(b-c)^3/(a-b)^3*ln(-b+_a)*c*a+2*b^4/(b-c)^3/(a-b)^3*ln(-b+_a)*c+4*c^3/(b-c)^3/(a-c)^3*ln(-c+_a)*a*b-2*c^4/(b-c)^3/(a-c)^3*ln(-c+_a)*a-2*c^4/(b-c)^3/(a-c)^3*ln(-c+_a)*b-b^4/(b-c)^2/(a-b)^2/(-b+_a))-_a^3*a1*(-a^4/(a-c)^2/(a-b)^2/(-a+_a)-2*a^4/(a-c)^3/(a-b)^3*ln(-a+_a)*b-2*a^4/(a-c)^3/(a-b)^3*ln(-a+_a)*c+4*a^3/(a-c)^3/(a-b)^3*ln(-a+_a)*c*b-c^4/(b-c)^2/(a-c)^2/(-c+_a)+2*b^4/(b-c)^3/(a-b)^3*ln(-b+_a)*a-4*b^3/(b-c)^3/(a-b)^3*ln(-b+_a)*c*a+2*b^4/(b-c)^3/(a-b)^3*ln(-b+_a)*c+4*c^3/(b-c)^3/(a-c)^3*ln(-c+_a)*a*b-2*c^4/(b-c)^3/(a-c)^3*ln(-c+_a)*a-2*c^4/(b-c)^3/(a-c)^3*ln(-c+_a)*b-b^4/(b-c)^2/(a-b)^2/(-b+_a))-_a^3*a0*(_a-a^6/(a-c)^2/(a-b)^2/(-a+_a)-b^6/(b-c)^2/(a-b)^2/(-b+_a)+2*a^7/(a-c)^3/(a-b)^3*ln(-a+_a)-4*a^6/(a-c)^3/(a-b)^3*ln(-a+_a)*b-4*a^6/(a-c)^3/(a-b)^3*ln(-a+_a)*c+6*a^5/(a-c)^3/(a-b)^3*ln(-a+_a)*c*b-c^6/(b-c)^2/(a-c)^2/(-c+_a)+4*b^6/(b-c)^3/(a-b)^3*ln(-b+_a)*a-6*b^5/(b-c)^3/(a-b)^3*ln(-b+_a)*c*a-2*b^7/(b-c)^3/(a-b)^3*ln(-b+_a)+4*b^6/(b-c)^3/(a-b)^3*ln(-b+_a)*c+6*c^5/(b-c)^3/(a-c)^3*ln(-c+_a)*a*b-4*c^6/(b-c)^3/(a-c)^3*ln(-c+_a)*a-4*c^6/(b-c)^3/(a-c)^3*ln(-c+_a)*b+2*c^7/(b-c)^3/(a-c)^3*ln(-c+_a))-_a^2*_C1*b-_a^2*_C1*c+_C1*_a*a*b+_C1*_a*a*c+_C1*_a*b*c-_C1*a*b*c)^(1/2),_a = y(x))-x-_C2 = 0, Intat(-1/(-_a^4*a0+(_C1+a0*(a+b+c))*_a^3+((-a-b-c)*_C1+((-a-b)*c-a*b)*a0+a1+2*a2+a3)*_a^2+(((a+b)*c+a*b)*_C1+a*a0*b*c+(-b-c)*a1+(-2*a-2*c)*a2-a3*(a+b))*_a-_C1*a*b*c+b*c*a1+a*(2*a2*c+a3*b))^(1/2),_a = y(x))-x-_C2 = 0