ODE
\[ (a-x) (b-x) (c-x) y'(x) \left (\text {a1}+\text {b1} x+\text {c1} x^2\right )+(a-x)^2 (b-x)^2 (c-x)^2 y''(x)+y(x) \left (\text {a2}+\text {b2} x+\text {c2} x^2\right )=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✗
cpu = 600.005 (sec), leaf count = 0 , timed out
$Aborted
Maple ✓
cpu = 21.024 (sec), leaf count = 10487 \[ \text {Too large to display} \] Mathematica raw input
DSolve[(a2 + b2*x + c2*x^2)*y[x] + (a - x)*(b - x)*(c - x)*(a1 + b1*x + c1*x^2)*y'[x] + (a - x)^2*(b - x)^2*(c - x)^2*y''[x] == 0,y[x],x]
Mathematica raw output
$Aborted
Maple raw input
dsolve((a-x)^2*(b-x)^2*(c-x)^2*diff(diff(y(x),x),x)+(a-x)*(b-x)*(c-x)*(c1*x^2+b1*x+a1)*diff(y(x),x)+(c2*x^2+b2*x+a2)*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = (x-b)^(1/2*(((c1+1)^2*b^4-2*(c1+1)*(a+c-b1)*b^3+(a^2+(-2*b1+(2*c1+4)*c)*a+c^2-2*b1*c+(2*c1+2)*a1+b1^2-4*c2)*b^2+(-2*a^2*c+(2*b1*c-2*c^2-2*a1)*a-2*a1*c+2*a1*b1-4*b2)*b+a^2*c^2+2*a*a1*c+a1^2-4*a2)^(1/2)+(-1-c1)*b^2+(a+c-b1)*b-a*c-a1)/(b-c)/(a-b))*(-c+x)^(1/2*(((c1+1)*c^2+(-a-b+b1)*c+a*b+a1)*(2*(c1+1)*(b-c)*(a-c)*((c1+1)^2*c^4-2*(c1+1)*(a+b-b1)*c^3+(a^2+((2*c1+4)*b-2*b1)*a+b^2-2*b*b1+(2*c1+2)*a1+b1^2-4*c2)*c^2+(-2*b*a^2+(-2*b^2+2*b*b1-2*a1)*a-2*a1*b+2*a1*b1-4*b2)*c+a^2*b^2+2*a*a1*b+a1^2-4*a2)^(1/2)+2*(c1+1)^2*c^4-2*((c1+2)*a+(c1+2)*b-b1)*(c1+1)*c^3+((c1^2+2*c1+2)*a^2+((4*c1^2+10*c1+8)*b-2*b1)*a+(c1^2+2*c1+2)*b^2-2*b*b1+2*a1*c1+b1^2+2*a1-4*c2)*c^2+(-2*b*(c1^2+2*c1+2)*a^2+((-2*c1^2-4*c1-4)*b^2+2*b*b1-2*a1)*a-2*a1*b+2*a1*b1-4*b2)*c+(c1^2+2*c1+2)*b^2*a^2+2*a*a1*b+a1^2-4*a2)^(1/2)+(c1+1)*(b-c)*(a-c)*((c1+1)^2*c^4-2*(c1+1)*(a+b-b1)*c^3+(a^2+((2*c1+4)*b-2*b1)*a+b^2-2*b*b1+(2*c1+2)*a1+b1^2-4*c2)*c^2+(-2*b*a^2+(-2*b^2+2*b*b1-2*a1)*a-2*a1*b+2*a1*b1-4*b2)*c+a^2*b^2+2*a*a1*b+a1^2-4*a2)^(1/2)+(c1+1)^2*c^4-2*(c1+1)*(a+b-b1)*c^3+(a^2+((2*c1+4)*b-2*b1)*a+b^2-2*b*b1+2*a1*c1+b1^2+2*a1-4*c2)*c^2+(-2*b*a^2+(-2*b^2+2*b*b1-2*a1)*a-2*a1*b+2*a1*b1-4*b2)*c+a^2*b^2+2*a*a1*b+a1^2-4*a2)/(2*(c1+1)*(b-c)*(a-c)*((c1+1)^2*c^4-2*(c1+1)*(a+b-b1)*c^3+(a^2+((2*c1+4)*b-2*b1)*a+b^2-2*b*b1+(2*c1+2)*a1+b1^2-4*c2)*c^2+(-2*b*a^2+(-2*b^2+2*b*b1-2*a1)*a-2*a1*b+2*a1*b1-4*b2)*c+a^2*b^2+2*a*a1*b+a1^2-4*a2)^(1/2)+2*(c1+1)^2*c^4-2*((c1+2)*a+(c1+2)*b-b1)*(c1+1)*c^3+((c1^2+2*c1+2)*a^2+((4*c1^2+10*c1+8)*b-2*b1)*a+(c1^2+2*c1+2)*b^2-2*b*b1+2*a1*c1+b1^2+2*a1-4*c2)*c^2+(-2*b*(c1^2+2*c1+2)*a^2+((-2*c1^2-4*c1-4)*b^2+2*b*b1-2*a1)*a-2*a1*b+2*a1*b1-4*b2)*c+(c1^2+2*c1+2)*b^2*a^2+2*a*a1*b+a1^2-4*a2)^(1/2)/(b-c)/(a-c))*(HeunG((a-c)/(a-b),1/4*(2*(((a-c)*((c1+1)^2*b^4-2*(c1+1)*(a+c-b1)*b^3+(a^2+(-2*b1+(2*c1+4)*c)*a+c^2-2*b1*c+(2*c1+2)*a1+b1^2-4*c2)*b^2+(-2*a^2*c+(2*b1*c-2*c^2-2*a1)*a-2*a1*c+2*a1*b1-4*b2)*b+a^2*c^2+2*a*a1*c+a1^2-4*a2)^(1/2)+(a-b)*(-b-c+2*a)*(b-c))*(a-c)*((c1+1)^2*a^4-2*(c1+1)*(b+c-b1)*a^3+((2*c1+2)*a1+b^2+(-2*b1+(2*c1+4)*c)*b+b1^2-2*b1*c+c^2-4*c2)*a^2+(-2*b^2*c+(2*b1*c-2*c^2-2*a1)*b-2*a1*c+2*a1*b1-4*b2)*a+b^2*c^2+2*a1*b*c+a1^2-4*a2)^(1/2)+(a-c)^3*(a-b)*((c1+1)^2*b^4-2*(c1+1)*(a+c-b1)*b^3+(a^2+(-2*b1+(2*c1+4)*c)*a+c^2-2*b1*c+(2*c1+2)*a1+b1^2-4*c2)*b^2+(-2*a^2*c+(2*b1*c-2*c^2-2*a1)*a-2*a1*c+2*a1*b1-4*b2)*b+a^2*c^2+2*a*a1*c+a1^2-4*a2)^(1/2)+(2*a^5+((c1^2-5)*c+c1^2*b+b1*c1-5*b)*a^4+(4*c^2+(-2*b*c1^2+b1*c1+12*b)*c+b1^2-4*c2+2*a1*c1+c1*b1*b+4*b^2)*a^3+(-c^3-9*b*c^2-3*(b1*c1+3*b)*b*c-6*b2+3*a1*b1-b^3)*a^2+(2*b*c^3+6*b^2*c^2+(2*b^3+(-2*a1*c1-b1^2+4*c2)*b+2*b2-a1*b1)*c+(-a1*b1+2*b2)*b+2*a1^2-8*a2)*a-b^2*c^3-b^3*c^2+((-a1*b1+2*b2)*b+4*a2-a1^2)*c-b*(a1^2-4*a2))*(b-c))*(2*(b-c)*(a-c)*((c1+1)^2*(a-b)^4*((c1+1)^2*c^4-2*(c1+1)*(a+b-b1)*c^3+(a^2+((2*c1+4)*b-2*b1)*a+b^2-2*b*b1+2*a1*c1+b1^2+2*a1-4*c2)*c^2+(-2*b*a^2+(-2*b^2+2*b*b1-2*a1)*a-2*a1*b+2*a1*b1-4*b2)*c+a^2*b^2+2*a*a1*b+a1^2-4*a2))^(1/2)+(a-b)^2*(2*(c1+1)^2*c^4-2*((c1+2)*a+(c1+2)*b-b1)*(c1+1)*c^3+((c1^2+2*c1+2)*a^2+((4*c1^2+10*c1+8)*b-2*b1)*a+(c1^2+2*c1+2)*b^2-2*b*b1+2*a1*c1+b1^2+2*a1-4*c2)*c^2+(-2*b*(c1^2+2*c1+2)*a^2+((-2*c1^2-4*c1-4)*b^2+2*b*b1-2*a1)*a-2*a1*b+2*a1*b1-4*b2)*c+(c1^2+2*c1+2)*b^2*a^2+2*a*a1*b+a1^2-4*a2))^(1/2)+(a-b)*(2*(a-c)*(a^2-a*b-a*c+c*b+((c1+1)^2*a^4-2*(c1+1)*(b+c-b1)*a^3+((2*c1+2)*a1+b^2+(-2*b1+(2*c1+4)*c)*b+b1^2-2*b1*c+c^2-4*c2)*a^2+(-2*b^2*c+(2*b1*c-2*c^2-2*a1)*b-2*a1*c+2*a1*b1-4*b2)*a+b^2*c^2+2*a1*b*c+a1^2-4*a2)^(1/2))*(b-c)*((c1+1)^2*(a-b)^4*((c1+1)^2*c^4-2*(c1+1)*(a+b-b1)*c^3+(a^2+((2*c1+4)*b-2*b1)*a+b^2-2*b*b1+2*a1*c1+b1^2+2*a1-4*c2)*c^2+(-2*b*a^2+(-2*b^2+2*b*b1-2*a1)*a-2*a1*b+2*a1*b1-4*b2)*c+a^2*b^2+2*a*a1*b+a1^2-4*a2))^(1/2)+(-(c1^2+2*c1-1)*(b-c)^2*a^4+2*((c1+1)*c^2+b1*(c1+3)*c+(c1-1)*b^2-b1*(c1+1)*b+2*a1)*(b-c)*a^3+((2*c1^2+4*c1+1)*c^4+2*((c1+1)*b+2*b1*c1+3*b1)*c^3+(2*(-3-2*c1)*b^2+2*b*b1+b1^2+2*a1-4*c2+2*a1*c1)*c^2+2*((-c1+1)*b^3-5*b^2*b1+(2*a1*c1+b1^2+4*a1-4*c2)*b+2*a1*b1-4*b2)*c+b^4+2*b^3*b1+(-2*a1*c1-b1^2-10*a1+4*c2)*b^2+2*a1^2-8*a2)*a^2+2*(-b*(2*c1^2+4*c1+1)*c^4+((2*c1+1)*b^2+(-4*b1*c1-5*b1)*b+a1)*c^3+((2*c1+1)*b^3+4*b^2*b1+(-4*a1*c1-2*b1^2-5*a1+8*c2)*b-a1*b1+2*b2)*c^2-b*(b^3-b^2*b1-a1*b+2*a1*b1-4*b2)*c+3*a1*b^3+(-a1*b1+2*b2)*b^2+(-2*a1^2+8*a2)*b)*a+b^2*(2*c1^2+4*c1+1)*c^4-2*((2*c1+1)*b^2-2*b1*(c1+1)*b+a1)*b*c^3+(b^4-4*b^3*b1+2*(2*a1*c1+b1^2+4*a1-4*c2)*b^2+4*a2-a1^2)*c^2+2*(-3*a1*b^3+(2*a1*b1-4*b2)*b^2+b*(a1^2-4*a2))*c+b^2*(a1^2-4*a2))*((c1+1)^2*a^4-2*(c1+1)*(b+c-b1)*a^3+((2*c1+2)*a1+b^2+(-2*b1+(2*c1+4)*c)*b+b1^2-2*b1*c+c^2-4*c2)*a^2+(-2*b^2*c+(2*b1*c-2*c^2-2*a1)*b-2*a1*c+2*a1*b1-4*b2)*a+b^2*c^2+2*a1*b*c+a1^2-4*a2)^(1/2)+(b-c)^2*((c1+1)^2*a^4-2*(c1+1)*(b+c-b1)*a^3+((2*c1+2)*a1+b^2+(-2*b1+(2*c1+4)*c)*b+b1^2-2*b1*c+c^2-4*c2)*a^2+(-2*b^2*c+(2*b1*c-2*c^2-2*a1)*b-2*a1*c+2*a1*b1-4*b2)*a+b^2*c^2+2*a1*b*c+a1^2-4*a2)^(3/2)+2*(a-b)^3*(a-c)*((b-c)^2*a^2-2*((-1-c1)*c^2+(b-b1)*c-a1)*(b-c)*a+(c1+1)^2*c^4-2*(c1+1)*(b-b1)*c^3+(2*a1*c1+b^2-2*b*b1+b1^2+2*a1-4*c2)*c^2+(-2*a1*b+2*a1*b1-4*b2)*c+a1^2-4*a2)))/(2*(b-c)*(a-c)*((c1+1)^2*(a-b)^4*((c1+1)^2*c^4-2*(c1+1)*(a+b-b1)*c^3+(a^2+((2*c1+4)*b-2*b1)*a+b^2-2*b*b1+2*a1*c1+b1^2+2*a1-4*c2)*c^2+(-2*b*a^2+(-2*b^2+2*b*b1-2*a1)*a-2*a1*b+2*a1*b1-4*b2)*c+a^2*b^2+2*a*a1*b+a1^2-4*a2))^(1/2)+(a-b)^2*(2*(c1+1)^2*c^4-2*((c1+2)*a+(c1+2)*b-b1)*(c1+1)*c^3+((c1^2+2*c1+2)*a^2+((4*c1^2+10*c1+8)*b-2*b1)*a+(c1^2+2*c1+2)*b^2-2*b*b1+2*a1*c1+b1^2+2*a1-4*c2)*c^2+(-2*b*(c1^2+2*c1+2)*a^2+((-2*c1^2-4*c1-4)*b^2+2*b*b1-2*a1)*a-2*a1*b+2*a1*b1-4*b2)*c+(c1^2+2*c1+2)*b^2*a^2+2*a*a1*b+a1^2-4*a2))^(1/2)/(b-c)/(a-c)^2/(a-b)^3,1/2*((2*(b-c)*(a-c)*((c1+1)^2*(a-b)^4*((c1+1)^2*c^4-2*(c1+1)*(a+b-b1)*c^3+(a^2+((2*c1+4)*b-2*b1)*a+b^2-2*b*b1+2*a1*c1+b1^2+2*a1-4*c2)*c^2+(-2*b*a^2+(-2*b^2+2*b*b1-2*a1)*a-2*a1*b+2*a1*b1-4*b2)*c+a^2*b^2+2*a*a1*b+a1^2-4*a2))^(1/2)+(a-b)^2*(2*(c1+1)^2*c^4-2*((c1+2)*a+(c1+2)*b-b1)*(c1+1)*c^3+((c1^2+2*c1+2)*a^2+((4*c1^2+10*c1+8)*b-2*b1)*a+(c1^2+2*c1+2)*b^2-2*b*b1+2*a1*c1+b1^2+2*a1-4*c2)*c^2+(-2*b*(c1^2+2*c1+2)*a^2+((-2*c1^2-4*c1-4)*b^2+2*b*b1-2*a1)*a-2*a1*b+2*a1*b1-4*b2)*c+(c1^2+2*c1+2)*b^2*a^2+2*a*a1*b+a1^2-4*a2))^(1/2)+(a-c)*((c1+1)^2*b^4-2*(c1+1)*(a+c-b1)*b^3+(a^2+(-2*b1+(2*c1+4)*c)*a+c^2-2*b1*c+(2*c1+2)*a1+b1^2-4*c2)*b^2+(-2*a^2*c+(2*b1*c-2*c^2-2*a1)*a-2*a1*c+2*a1*b1-4*b2)*b+a^2*c^2+2*a*a1*c+a1^2-4*a2)^(1/2)+(b-c)*((c1+1)^2*a^4-2*(c1+1)*(b+c-b1)*a^3+((2*c1+2)*a1+b^2+(-2*b1+(2*c1+4)*c)*b+b1^2-2*b1*c+c^2-4*c2)*a^2+(-2*b^2*c+(2*b1*c-2*c^2-2*a1)*b-2*a1*c+2*a1*b1-4*b2)*a+b^2*c^2+2*a1*b*c+a1^2-4*a2)^(1/2)+(2*a-2*b)*c^2+(-2*a^2+2*b^2)*c+2*b*a^2-2*a*b^2)/(b-c)/(a-c)/(a-b),-1/2*(((-a+c)*((c1+1)^2*b^4-2*(c1+1)*(a+c-b1)*b^3+(a^2+(-2*b1+(2*c1+4)*c)*a+c^2-2*b1*c+(2*c1+2)*a1+b1^2-4*c2)*b^2+(-2*a^2*c+(2*b1*c-2*c^2-2*a1)*a-2*a1*c+2*a1*b1-4*b2)*b+a^2*c^2+2*a*a1*c+a1^2-4*a2)^(1/2)-2*(1/2*((c1+1)^2*a^4-2*(c1+1)*(b+c-b1)*a^3+((2*c1+2)*a1+b^2+(-2*b1+(2*c1+4)*c)*b+b1^2-2*b1*c+c^2-4*c2)*a^2+(-2*b^2*c+(2*b1*c-2*c^2-2*a1)*b-2*a1*c+2*a1*b1-4*b2)*a+b^2*c^2+2*a1*b*c+a1^2-4*a2)^(1/2)+(a-b)*(a-c))*(b-c))*(2*(b-c)*(a-c)*((c1+1)^2*(a-b)^4*((c1+1)^2*c^4-2*(c1+1)*(a+b-b1)*c^3+(a^2+((2*c1+4)*b-2*b1)*a+b^2-2*b*b1+2*a1*c1+b1^2+2*a1-4*c2)*c^2+(-2*b*a^2+(-2*b^2+2*b*b1-2*a1)*a-2*a1*b+2*a1*b1-4*b2)*c+a^2*b^2+2*a*a1*b+a1^2-4*a2))^(1/2)+(a-b)^2*(2*(c1+1)^2*c^4-2*((c1+2)*a+(c1+2)*b-b1)*(c1+1)*c^3+((c1^2+2*c1+2)*a^2+((4*c1^2+10*c1+8)*b-2*b1)*a+(c1^2+2*c1+2)*b^2-2*b*b1+2*a1*c1+b1^2+2*a1-4*c2)*c^2+(-2*b*(c1^2+2*c1+2)*a^2+((-2*c1^2-4*c1-4)*b^2+2*b*b1-2*a1)*a-2*a1*b+2*a1*b1-4*b2)*c+(c1^2+2*c1+2)*b^2*a^2+2*a*a1*b+a1^2-4*a2))^(1/2)+(a-b)^2*(((a-c)*b-a*c)*((a-c)*b-c*(a-2*c))*c1^2+(2*(a-c)^2*b^2-4*(a-c)*(a-1/2*c)*c*b+2*c^2*(a^2-a*c-b1*c-a1))*c1-2*(b1*c+a1)*(a-c)*b+(2*b1*c^2+2*a1*c)*a-2*b1*c^3+(-b1^2-2*a1+4*c2)*c^2+(-2*a1*b1+4*b2)*c-a1^2+4*a2))/(2*(b-c)*(a-c)*((c1+1)^2*(a-b)^4*((c1+1)^2*c^4-2*(c1+1)*(a+b-b1)*c^3+(a^2+((2*c1+4)*b-2*b1)*a+b^2-2*b*b1+2*a1*c1+b1^2+2*a1-4*c2)*c^2+(-2*b*a^2+(-2*b^2+2*b*b1-2*a1)*a-2*a1*b+2*a1*b1-4*b2)*c+a^2*b^2+2*a*a1*b+a1^2-4*a2))^(1/2)+(a-b)^2*(2*(c1+1)^2*c^4-2*((c1+2)*a+(c1+2)*b-b1)*(c1+1)*c^3+((c1^2+2*c1+2)*a^2+((4*c1^2+10*c1+8)*b-2*b1)*a+(c1^2+2*c1+2)*b^2-2*b*b1+2*a1*c1+b1^2+2*a1-4*c2)*c^2+(-2*b*(c1^2+2*c1+2)*a^2+((-2*c1^2-4*c1-4)*b^2+2*b*b1-2*a1)*a-2*a1*b+2*a1*b1-4*b2)*c+(c1^2+2*c1+2)*b^2*a^2+2*a*a1*b+a1^2-4*a2))^(1/2)/(b-c)/(a-c)/(a-b),(((c1+1)^2*a^4-2*(c1+1)*(b+c-b1)*a^3+((2*c1+2)*a1+b^2+(-2*b1+(2*c1+4)*c)*b+b1^2-2*b1*c+c^2-4*c2)*a^2+(-2*b^2*c+(2*b1*c-2*c^2-2*a1)*b-2*a1*c+2*a1*b1-4*b2)*a+b^2*c^2+2*a1*b*c+a1^2-4*a2)^(1/2)+a^2+(-b-c)*a+c*b)/(a-c)/(a-b),(((c1+1)^2*b^4-2*(c1+1)*(a+c-b1)*b^3+(a^2+(-2*b1+(2*c1+4)*c)*a+c^2-2*b1*c+(2*c1+2)*a1+b1^2-4*c2)*b^2+(-2*a^2*c+(2*b1*c-2*c^2-2*a1)*a-2*a1*c+2*a1*b1-4*b2)*b+a^2*c^2+2*a*a1*c+a1^2-4*a2)^(1/2)-b^2+(a+c)*b-a*c)/(b-c)/(a-b),(a-x)/(a-b))*(x-a)^(1/2*(((c1+1)^2*a^4-2*(c1+1)*(b+c-b1)*a^3+((2*c1+2)*a1+b^2+(-2*b1+(2*c1+4)*c)*b+b1^2-2*b1*c+c^2-4*c2)*a^2+(-2*b^2*c+(2*b1*c-2*c^2-2*a1)*b-2*a1*c+2*a1*b1-4*b2)*a+b^2*c^2+2*a1*b*c+a1^2-4*a2)^(1/2)+(c1+1)*a^2+(-b-c+b1)*a+c*b+a1)/(a-c)/(a-b))*_C1+(x-a)^(1/2*(-((c1+1)^2*a^4-2*(c1+1)*(b+c-b1)*a^3+((2*c1+2)*a1+b^2+(-2*b1+(2*c1+4)*c)*b+b1^2-2*b1*c+c^2-4*c2)*a^2+(-2*b^2*c+(2*b1*c-2*c^2-2*a1)*b-2*a1*c+2*a1*b1-4*b2)*a+b^2*c^2+2*a1*b*c+a1^2-4*a2)^(1/2)+(c1+1)*a^2+(-b-c+b1)*a+c*b+a1)/(a-c)/(a-b))*HeunG((a-c)/(a-b),1/2*((-2*((1/2*a-1/2*c)*((c1+1)^2*b^4-2*(c1+1)*(a+c-b1)*b^3+(a^2+(-2*b1+(2*c1+4)*c)*a+c^2-2*b1*c+(2*c1+2)*a1+b1^2-4*c2)*b^2+(-2*a^2*c+(2*b1*c-2*c^2-2*a1)*a-2*a1*c+2*a1*b1-4*b2)*b+a^2*c^2+2*a*a1*c+a1^2-4*a2)^(1/2)+(a-b)*(a-1/2*b-1/2*c)*(b-c))*(a-c)*((c1+1)^2*a^4-2*(c1+1)*(b+c-b1)*a^3+((2*c1+2)*a1+b^2+(-2*b1+(2*c1+4)*c)*b+b1^2-2*b1*c+c^2-4*c2)*a^2+(-2*b^2*c+(2*b1*c-2*c^2-2*a1)*b-2*a1*c+2*a1*b1-4*b2)*a+b^2*c^2+2*a1*b*c+a1^2-4*a2)^(1/2)+(a-c)^3*(a-b)*((c1+1)^2*b^4-2*(c1+1)*(a+c-b1)*b^3+(a^2+(-2*b1+(2*c1+4)*c)*a+c^2-2*b1*c+(2*c1+2)*a1+b1^2-4*c2)*b^2+(-2*a^2*c+(2*b1*c-2*c^2-2*a1)*a-2*a1*c+2*a1*b1-4*b2)*b+a^2*c^2+2*a*a1*c+a1^2-4*a2)^(1/2)+2*(-1/2*(a-b)^2*c^3+2*(a-b)^2*(a-1/4*b)*c^2+((1/2*c1^2-5/2)*a^4+(-c1^2*b+1/2*b1*c1+6*b)*a^3-9/2*(1/3*b1*c1+b)*b*a^2+(b2-c1*b*a1-1/2*b1^2*b+2*c2*b-1/2*a1*b1+b^3)*a+2*a2-1/2*a1^2+b*b2-1/2*a1*b*b1)*c+a^5+(1/2*c1^2*b+1/2*b1*c1-5/2*b)*a^4+((a1+1/2*b*b1)*c1+1/2*b1^2-2*c2+2*b^2)*a^3+(-3*b2+3/2*a1*b1-1/2*b^3)*a^2+(a1^2-4*a2+b*b2-1/2*a1*b*b1)*a-1/2*b*(a1^2-4*a2))*(b-c))*(2*(b-c)*(a-c)*((c1+1)^2*(a-b)^4*((c1+1)^2*c^4-2*(c1+1)*(a+b-b1)*c^3+(a^2+((2*c1+4)*b-2*b1)*a+b^2-2*b*b1+2*a1*c1+b1^2+2*a1-4*c2)*c^2+(-2*b*a^2+(-2*b^2+2*b*b1-2*a1)*a-2*a1*b+2*a1*b1-4*b2)*c+a^2*b^2+2*a*a1*b+a1^2-4*a2))^(1/2)+(a-b)^2*(2*(c1+1)^2*c^4-2*((c1+2)*a+(c1+2)*b-b1)*(c1+1)*c^3+((c1^2+2*c1+2)*a^2+((4*c1^2+10*c1+8)*b-2*b1)*a+(c1^2+2*c1+2)*b^2-2*b*b1+2*a1*c1+b1^2+2*a1-4*c2)*c^2+(-2*b*(c1^2+2*c1+2)*a^2+((-2*c1^2-4*c1-4)*b^2+2*b*b1-2*a1)*a-2*a1*b+2*a1*b1-4*b2)*c+(c1^2+2*c1+2)*b^2*a^2+2*a*a1*b+a1^2-4*a2))^(1/2)+(a-b)*((-((c1+1)^2*a^4-2*(c1+1)*(b+c-b1)*a^3+((2*c1+2)*a1+b^2+(-2*b1+(2*c1+4)*c)*b+b1^2-2*b1*c+c^2-4*c2)*a^2+(-2*b^2*c+(2*b1*c-2*c^2-2*a1)*b-2*a1*c+2*a1*b1-4*b2)*a+b^2*c^2+2*a1*b*c+a1^2-4*a2)^(1/2)+(a-b)*(a-c))*(a-c)*(b-c)*((c1+1)^2*(a-b)^4*((c1+1)^2*c^4-2*(c1+1)*(a+b-b1)*c^3+(a^2+((2*c1+4)*b-2*b1)*a+b^2-2*b*b1+2*a1*c1+b1^2+2*a1-4*c2)*c^2+(-2*b*a^2+(-2*b^2+2*b*b1-2*a1)*a-2*a1*b+2*a1*b1-4*b2)*c+a^2*b^2+2*a*a1*b+a1^2-4*a2))^(1/2)+1/2*(b-c)^2*((c1+1)^2*a^4-2*(c1+1)*(b+c-b1)*a^3+((2*c1+2)*a1+b^2+(-2*b1+(2*c1+4)*c)*b+b1^2-2*b1*c+c^2-4*c2)*a^2+(-2*b^2*c+(2*b1*c-2*c^2-2*a1)*b-2*a1*c+2*a1*b1-4*b2)*a+b^2*c^2+2*a1*b*c+a1^2-4*a2)^(3/2)+(-(c1^2+2*c1+3/2)*(a-b)^2*c^4+3*(a-b)*((c1+1)*a^2-2/3*b1*(c1+1/2)*a-2/3*b*(b-b1)*c1-b^2+2/3*b*b1+1/3*a1)*c^3+((-3/2-c1-1/2*c1^2)*a^4+((-3*b-b1)*c1-3*b+b1)*a^3+((6*b^2-3*a1)*c1-3*b*b1-3/2*b1^2-3*a1+6*c2+9*b^2)*a^2+((-2*b^3+4*a1*b)*c1+(3*b-b1)*a1-3*b^3+2*b1^2*b-8*c2*b+2*b2)*a-1/2*a1^2+2*a2-3/2*b^4-2*a1*b^2*c1+2*b^3*b1-b^2*b1^2+4*b^2*c2)*c^2+(b*(c1^2+2*c1+3)*a^4+(-b*(b-2*b1)*c1-3*b^2+2*a1)*a^3+((-b^3+2*a1*b)*c1-3*b^3+3*b^2*b1+b1^2*b-4*c2*b-2*a1*b1+4*b2)*a^2+3*((-b+2*b1)*a1+b^3-b^2*b1-4*b2)*b*a+(a1^2+b*(b-2*b1)*a1+4*b*b2-4*a2)*b)*c-1/2*b^2*(c1^2+2*c1+3)*a^4+b*(b*(b-b1)*c1+3*b^2-b*b1-2*a1)*a^3+(-a1*b^2*c1+b^3*b1+4*a2-3/2*b^4-a1^2+3*a1*b^2-1/2*b^2*b1^2+2*b^2*c2)*a^2-(-2*a1^2+b*(b+b1)*a1-2*b*b2+8*a2)*b*a-3/2*b^2*(a1^2-4*a2))*((c1+1)^2*a^4-2*(c1+1)*(b+c-b1)*a^3+((2*c1+2)*a1+b^2+(-2*b1+(2*c1+4)*c)*b+b1^2-2*b1*c+c^2-4*c2)*a^2+(-2*b^2*c+(2*b1*c-2*c^2-2*a1)*b-2*a1*c+2*a1*b1-4*b2)*a+b^2*c^2+2*a1*b*c+a1^2-4*a2)^(1/2)+(a-b)^3*(a-c)*((c1+1)^2*c^4-2*(c1+1)*(a+b-b1)*c^3+(a^2+(2*b*c1+4*b-2*b1)*a+b^2-2*b*b1+2*a1*c1+b1^2+2*a1-4*c2)*c^2+(-2*b*a^2+(-2*b^2+2*b*b1-2*a1)*a+(-2*b+2*b1)*a1-4*b2)*c+a^2*b^2+2*a*a1*b+a1^2-4*a2)))/(2*(b-c)*(a-c)*((c1+1)^2*(a-b)^4*((c1+1)^2*c^4-2*(c1+1)*(a+b-b1)*c^3+(a^2+((2*c1+4)*b-2*b1)*a+b^2-2*b*b1+2*a1*c1+b1^2+2*a1-4*c2)*c^2+(-2*b*a^2+(-2*b^2+2*b*b1-2*a1)*a-2*a1*b+2*a1*b1-4*b2)*c+a^2*b^2+2*a*a1*b+a1^2-4*a2))^(1/2)+(a-b)^2*(2*(c1+1)^2*c^4-2*((c1+2)*a+(c1+2)*b-b1)*(c1+1)*c^3+((c1^2+2*c1+2)*a^2+((4*c1^2+10*c1+8)*b-2*b1)*a+(c1^2+2*c1+2)*b^2-2*b*b1+2*a1*c1+b1^2+2*a1-4*c2)*c^2+(-2*b*(c1^2+2*c1+2)*a^2+((-2*c1^2-4*c1-4)*b^2+2*b*b1-2*a1)*a-2*a1*b+2*a1*b1-4*b2)*c+(c1^2+2*c1+2)*b^2*a^2+2*a*a1*b+a1^2-4*a2))^(1/2)/(b-c)/(a-c)^2/(a-b)^3,1/2*((2*(b-c)*(a-c)*((c1+1)^2*(a-b)^4*((c1+1)^2*c^4-2*(c1+1)*(a+b-b1)*c^3+(a^2+((2*c1+4)*b-2*b1)*a+b^2-2*b*b1+2*a1*c1+b1^2+2*a1-4*c2)*c^2+(-2*b*a^2+(-2*b^2+2*b*b1-2*a1)*a-2*a1*b+2*a1*b1-4*b2)*c+a^2*b^2+2*a*a1*b+a1^2-4*a2))^(1/2)+(a-b)^2*(2*(c1+1)^2*c^4-2*((c1+2)*a+(c1+2)*b-b1)*(c1+1)*c^3+((c1^2+2*c1+2)*a^2+((4*c1^2+10*c1+8)*b-2*b1)*a+(c1^2+2*c1+2)*b^2-2*b*b1+2*a1*c1+b1^2+2*a1-4*c2)*c^2+(-2*b*(c1^2+2*c1+2)*a^2+((-2*c1^2-4*c1-4)*b^2+2*b*b1-2*a1)*a-2*a1*b+2*a1*b1-4*b2)*c+(c1^2+2*c1+2)*b^2*a^2+2*a*a1*b+a1^2-4*a2))^(1/2)+(a-c)*((c1+1)^2*b^4-2*(c1+1)*(a+c-b1)*b^3+(a^2+(-2*b1+(2*c1+4)*c)*a+c^2-2*b1*c+(2*c1+2)*a1+b1^2-4*c2)*b^2+(-2*a^2*c+(2*b1*c-2*c^2-2*a1)*a-2*a1*c+2*a1*b1-4*b2)*b+a^2*c^2+2*a*a1*c+a1^2-4*a2)^(1/2)+(-b+c)*((c1+1)^2*a^4-2*(c1+1)*(b+c-b1)*a^3+((2*c1+2)*a1+b^2+(-2*b1+(2*c1+4)*c)*b+b1^2-2*b1*c+c^2-4*c2)*a^2+(-2*b^2*c+(2*b1*c-2*c^2-2*a1)*b-2*a1*c+2*a1*b1-4*b2)*a+b^2*c^2+2*a1*b*c+a1^2-4*a2)^(1/2)+(2*a-2*b)*c^2+(-2*a^2+2*b^2)*c+2*b*a^2-2*a*b^2)/(b-c)/(a-c)/(a-b),-1/2*(((b-c)*((c1+1)^2*a^4-2*(c1+1)*(b+c-b1)*a^3+((2*c1+2)*a1+b^2+(-2*b1+(2*c1+4)*c)*b+b1^2-2*b1*c+c^2-4*c2)*a^2+(-2*b^2*c+(2*b1*c-2*c^2-2*a1)*b-2*a1*c+2*a1*b1-4*b2)*a+b^2*c^2+2*a1*b*c+a1^2-4*a2)^(1/2)-2*(1/2*((c1+1)^2*b^4-2*(c1+1)*(a+c-b1)*b^3+(a^2+(-2*b1+(2*c1+4)*c)*a+c^2-2*b1*c+(2*c1+2)*a1+b1^2-4*c2)*b^2+(-2*a^2*c+(2*b1*c-2*c^2-2*a1)*a-2*a1*c+2*a1*b1-4*b2)*b+a^2*c^2+2*a*a1*c+a1^2-4*a2)^(1/2)+(b-c)*(a-b))*(a-c))*(2*(b-c)*(a-c)*((c1+1)^2*(a-b)^4*((c1+1)^2*c^4-2*(c1+1)*(a+b-b1)*c^3+(a^2+((2*c1+4)*b-2*b1)*a+b^2-2*b*b1+2*a1*c1+b1^2+2*a1-4*c2)*c^2+(-2*b*a^2+(-2*b^2+2*b*b1-2*a1)*a-2*a1*b+2*a1*b1-4*b2)*c+a^2*b^2+2*a*a1*b+a1^2-4*a2))^(1/2)+(a-b)^2*(2*(c1+1)^2*c^4-2*((c1+2)*a+(c1+2)*b-b1)*(c1+1)*c^3+((c1^2+2*c1+2)*a^2+((4*c1^2+10*c1+8)*b-2*b1)*a+(c1^2+2*c1+2)*b^2-2*b*b1+2*a1*c1+b1^2+2*a1-4*c2)*c^2+(-2*b*(c1^2+2*c1+2)*a^2+((-2*c1^2-4*c1-4)*b^2+2*b*b1-2*a1)*a-2*a1*b+2*a1*b1-4*b2)*c+(c1^2+2*c1+2)*b^2*a^2+2*a*a1*b+a1^2-4*a2))^(1/2)+(a-b)^2*(c1*(b-c)^2*(c1+2)*a^2-2*((-c1^2-c1)*c^2+(b*c1^2+2*b*c1+b1)*c+a1)*(b-c)*a-2*(c1+1)*(b*c1+b1)*c^3+(b^2*c1^2+(2*b^2-2*a1)*c1+2*b*b1-b1^2-2*a1+4*c2)*c^2+(2*a1*b-2*a1*b1+4*b2)*c-a1^2+4*a2))/(2*(b-c)*(a-c)*((c1+1)^2*(a-b)^4*((c1+1)^2*c^4-2*(c1+1)*(a+b-b1)*c^3+(a^2+((2*c1+4)*b-2*b1)*a+b^2-2*b*b1+2*a1*c1+b1^2+2*a1-4*c2)*c^2+(-2*b*a^2+(-2*b^2+2*b*b1-2*a1)*a-2*a1*b+2*a1*b1-4*b2)*c+a^2*b^2+2*a*a1*b+a1^2-4*a2))^(1/2)+(a-b)^2*(2*(c1+1)^2*c^4-2*((c1+2)*a+(c1+2)*b-b1)*(c1+1)*c^3+((c1^2+2*c1+2)*a^2+((4*c1^2+10*c1+8)*b-2*b1)*a+(c1^2+2*c1+2)*b^2-2*b*b1+2*a1*c1+b1^2+2*a1-4*c2)*c^2+(-2*b*(c1^2+2*c1+2)*a^2+((-2*c1^2-4*c1-4)*b^2+2*b*b1-2*a1)*a-2*a1*b+2*a1*b1-4*b2)*c+(c1^2+2*c1+2)*b^2*a^2+2*a*a1*b+a1^2-4*a2))^(1/2)/(b-c)/(a-c)/(a-b),(-((c1+1)^2*a^4-2*(c1+1)*(b+c-b1)*a^3+((2*c1+2)*a1+b^2+(-2*b1+(2*c1+4)*c)*b+b1^2-2*b1*c+c^2-4*c2)*a^2+(-2*b^2*c+(2*b1*c-2*c^2-2*a1)*b-2*a1*c+2*a1*b1-4*b2)*a+b^2*c^2+2*a1*b*c+a1^2-4*a2)^(1/2)+a^2+(-b-c)*a+c*b)/(a-c)/(a-b),(((c1+1)^2*b^4-2*(c1+1)*(a+c-b1)*b^3+(a^2+(-2*b1+(2*c1+4)*c)*a+c^2-2*b1*c+(2*c1+2)*a1+b1^2-4*c2)*b^2+(-2*a^2*c+(2*b1*c-2*c^2-2*a1)*a-2*a1*c+2*a1*b1-4*b2)*b+a^2*c^2+2*a*a1*c+a1^2-4*a2)^(1/2)-b^2+(a+c)*b-a*c)/(b-c)/(a-b),(a-x)/(a-b))*_C2)