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 = 170.067 (sec), leaf count = 1
\[\text {$\$$Aborted}\]
Maple ✓
cpu = 0.252 (sec), leaf count = 374
\[ \left \{ y \left ( x \right ) = \left ( -1+x \right ) ^{{\frac {{\it a1}}{2}}+{\frac {{\it b2}}{2}}-{\frac {1}{2}\sqrt {{{\it a1}}^{2}+ \left ( 2\,{\it b2}+2 \right ) {\it a1}+{{\it b2}}^{2}-4\,{\it a2}-2\,{\it b2}-4\,{\it c2}+1}}+{\frac {1}{2}}} \left ( {\mbox {$_2$F$_1$}(-{\frac {1}{2}\sqrt {{{\it a1}}^{2}+ \left ( 2\,{\it b2}+2 \right ) {\it a1}+{{\it b2}}^{2}-4\,{\it a2}-2\,{\it b2}-4\,{\it c2}+1}}+{\frac {1}{2}}+{\frac {1}{2}\sqrt {{{\it a1}}^{2}-2\,{\it a1}-4\,{\it a2}+1}}+{\frac {1}{2}\sqrt {{{\it b2}}^{2}+2\,{\it b2}-4\,{\it c2}+1}},-{\frac {1}{2}\sqrt {{{\it a1}}^{2}+ \left ( 2\,{\it b2}+2 \right ) {\it a1}+{{\it b2}}^{2}-4\,{\it a2}-2\,{\it b2}-4\,{\it c2}+1}}+{\frac {1}{2}}+{\frac {1}{2}\sqrt {{{\it a1}}^{2}-2\,{\it a1}-4\,{\it a2}+1}}-{\frac {1}{2}\sqrt {{{\it b2}}^{2}+2\,{\it b2}-4\,{\it c2}+1}};\,1+\sqrt {{{\it a1}}^{2}-2\,{\it a1}-4\,{\it a2}+1};\,x)}{x}^{-{\frac {{\it a1}}{2}}+{\frac {1}{2}\sqrt {{{\it a1}}^{2}-2\,{\it a1}-4\,{\it a2}+1}}+{\frac {1}{2}}}{\it \_C1}+{\mbox {$_2$F$_1$}(-{\frac {1}{2}\sqrt {{{\it a1}}^{2}+ \left ( 2\,{\it b2}+2 \right ) {\it a1}+{{\it b2}}^{2}-4\,{\it a2}-2\,{\it b2}-4\,{\it c2}+1}}+{\frac {1}{2}}-{\frac {1}{2}\sqrt {{{\it a1}}^{2}-2\,{\it a1}-4\,{\it a2}+1}}-{\frac {1}{2}\sqrt {{{\it b2}}^{2}+2\,{\it b2}-4\,{\it c2}+1}},-{\frac {1}{2}\sqrt {{{\it a1}}^{2}+ \left ( 2\,{\it b2}+2 \right ) {\it a1}+{{\it b2}}^{2}-4\,{\it a2}-2\,{\it b2}-4\,{\it c2}+1}}+{\frac {1}{2}}-{\frac {1}{2}\sqrt {{{\it a1}}^{2}-2\,{\it a1}-4\,{\it a2}+1}}+{\frac {1}{2}\sqrt {{{\it b2}}^{2}+2\,{\it b2}-4\,{\it c2}+1}};\,1-\sqrt {{{\it a1}}^{2}-2\,{\it a1}-4\,{\it a2}+1};\,x)}{x}^{-{\frac {{\it a1}}{2}}-{\frac {1}{2}\sqrt {{{\it a1}}^{2}-2\,{\it a1}-4\,{\it a2}+1}}+{\frac {1}{2}}}{\it \_C2} \right ) \right \} \] 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),'implicit')
Maple raw output
y(x) = (-1+x)^(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)*x^(-1/2*a1+1/2*(a1^2-2*a1-4*a2+1)^(1/2)+1/2)*_C1+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)*x^(-1/2*a1-1/2*(a1^2-2*a1-4*a2+1)^(1/2)+1/2)*_C2)