ODE
\[ (1-x) x (\text {a1}+\text {b2} x) y'(x)+y(x) \left (\text {a2}+\text {b2} x+\text {c2} x^2\right )+(1-x)^2 x^2 y''(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 130.481 (sec), leaf count = 1
\[\text {$\$$Aborted}\]
Maple ✓
cpu = 0.617 (sec), leaf count = 413
\[\left [y \left (x \right ) = \textit {\_C1} \,x^{-\frac {\mathit {a1}}{2}+\frac {1}{2}+\frac {\sqrt {\mathit {a1}^{2}-2 \mathit {a1} -4 \mathit {a2} +1}}{2}} \left (x -1\right )^{\frac {\mathit {a1}}{2}+\frac {\mathit {b2}}{2}-\frac {\sqrt {\mathit {a1}^{2}+\left (2 \mathit {b2} +2\right ) \mathit {a1} +\mathit {b2}^{2}-4 \mathit {a2} -2 \mathit {b2} -4 \mathit {c2} +1}}{2}+\frac {1}{2}} \hypergeom \left (\left [-\frac {\sqrt {\mathit {a1}^{2}+\left (2 \mathit {b2} +2\right ) \mathit {a1} +\mathit {b2}^{2}-4 \mathit {a2} -2 \mathit {b2} -4 \mathit {c2} +1}}{2}+\frac {1}{2}+\frac {\sqrt {\mathit {a1}^{2}-2 \mathit {a1} -4 \mathit {a2} +1}}{2}-\frac {\sqrt {\mathit {b2}^{2}+2 \mathit {b2} -4 \mathit {c2} +1}}{2}, -\frac {\sqrt {\mathit {a1}^{2}+\left (2 \mathit {b2} +2\right ) \mathit {a1} +\mathit {b2}^{2}-4 \mathit {a2} -2 \mathit {b2} -4 \mathit {c2} +1}}{2}+\frac {1}{2}+\frac {\sqrt {\mathit {a1}^{2}-2 \mathit {a1} -4 \mathit {a2} +1}}{2}+\frac {\sqrt {\mathit {b2}^{2}+2 \mathit {b2} -4 \mathit {c2} +1}}{2}\right ], \left [1+\sqrt {\mathit {a1}^{2}-2 \mathit {a1} -4 \mathit {a2} +1}\right ], x\right )+\textit {\_C2} \,x^{-\frac {\mathit {a1}}{2}+\frac {1}{2}-\frac {\sqrt {\mathit {a1}^{2}-2 \mathit {a1} -4 \mathit {a2} +1}}{2}} \left (x -1\right )^{\frac {\mathit {a1}}{2}+\frac {\mathit {b2}}{2}-\frac {\sqrt {\mathit {a1}^{2}+\left (2 \mathit {b2} +2\right ) \mathit {a1} +\mathit {b2}^{2}-4 \mathit {a2} -2 \mathit {b2} -4 \mathit {c2} +1}}{2}+\frac {1}{2}} \hypergeom \left (\left [-\frac {\sqrt {\mathit {a1}^{2}+\left (2 \mathit {b2} +2\right ) \mathit {a1} +\mathit {b2}^{2}-4 \mathit {a2} -2 \mathit {b2} -4 \mathit {c2} +1}}{2}+\frac {1}{2}-\frac {\sqrt {\mathit {a1}^{2}-2 \mathit {a1} -4 \mathit {a2} +1}}{2}+\frac {\sqrt {\mathit {b2}^{2}+2 \mathit {b2} -4 \mathit {c2} +1}}{2}, -\frac {\sqrt {\mathit {a1}^{2}+\left (2 \mathit {b2} +2\right ) \mathit {a1} +\mathit {b2}^{2}-4 \mathit {a2} -2 \mathit {b2} -4 \mathit {c2} +1}}{2}+\frac {1}{2}-\frac {\sqrt {\mathit {a1}^{2}-2 \mathit {a1} -4 \mathit {a2} +1}}{2}-\frac {\sqrt {\mathit {b2}^{2}+2 \mathit {b2} -4 \mathit {c2} +1}}{2}\right ], \left [-\sqrt {\mathit {a1}^{2}-2 \mathit {a1} -4 \mathit {a2} +1}+1\right ], x\right )\right ]\] Mathematica raw input
DSolve[(a2 + b2*x + c2*x^2)*y[x] + (1 - x)*x*(a1 + b2*x)*y'[x] + (1 - x)^2*x^2*y''[x] == 0,y[x],x]
Mathematica raw output
$Aborted
Maple raw input
dsolve(x^2*(1-x)^2*diff(diff(y(x),x),x)+x*(1-x)*(b2*x+a1)*diff(y(x),x)+(c2*x^2+b2*x+a2)*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*x^(-1/2*a1+1/2+1/2*(a1^2-2*a1-4*a2+1)^(1/2))*(x-1)^(1/2*a1+1/2*b2-1/2*(a1^2+(2*b2+2)*a1+b2^2-4*a2-2*b2-4*c2+1)^(1/2)+1/2)*hypergeom([-1/2*(a1^2+(2*b2+2)*a1+b2^2-4*a2-2*b2-4*c2+1)^(1/2)+1/2+1/2*(a1^2-2*a1-4*a2+1)^(1/2)-1/2*(b2^2+2*b2-4*c2+1)^(1/2), -1/2*(a1^2+(2*b2+2)*a1+b2^2-4*a2-2*b2-4*c2+1)^(1/2)+1/2+1/2*(a1^2-2*a1-4*a2+1)^(1/2)+1/2*(b2^2+2*b2-4*c2+1)^(1/2)],[1+(a1^2-2*a1-4*a2+1)^(1/2)],x)+_C2*x^(-1/2*a1+1/2-1/2*(a1^2-2*a1-4*a2+1)^(1/2))*(x-1)^(1/2*a1+1/2*b2-1/2*(a1^2+(2*b2+2)*a1+b2^2-4*a2-2*b2-4*c2+1)^(1/2)+1/2)*hypergeom([-1/2*(a1^2+(2*b2+2)*a1+b2^2-4*a2-2*b2-4*c2+1)^(1/2)+1/2-1/2*(a1^2-2*a1-4*a2+1)^(1/2)+1/2*(b2^2+2*b2-4*c2+1)^(1/2), -1/2*(a1^2+(2*b2+2)*a1+b2^2-4*a2-2*b2-4*c2+1)^(1/2)+1/2-1/2*(a1^2-2*a1-4*a2+1)^(1/2)-1/2*(b2^2+2*b2-4*c2+1)^(1/2)],[-(a1^2-2*a1-4*a2+1)^(1/2)+1],x)]