ODE
\[ y(x) \left (a+b x+c x^2\right )+(1-x)^2 x^2 y''(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 9.72974 (sec), leaf count = 1
\[\text {$\$$Aborted}\]
Maple ✓
cpu = 0.119 (sec), leaf count = 225
\[ \left \{ y \left ( x \right ) = \left ( -1+x \right ) ^{-{\frac {1}{2}\sqrt {1-4\,a-4\,b-4\,c}}+{\frac {1}{2}}} \left ( {x}^{-{\frac {1}{2}\sqrt {1-4\,a}}+{\frac {1}{2}}}{\mbox {$_2$F$_1$}(-{\frac {1}{2}\sqrt {1-4\,a-4\,b-4\,c}}-{\frac {1}{2}\sqrt {1-4\,a}}+{\frac {1}{2}}+{\frac {1}{2}\sqrt {1-4\,c}},-{\frac {1}{2}\sqrt {1-4\,a-4\,b-4\,c}}-{\frac {1}{2}\sqrt {1-4\,a}}+{\frac {1}{2}}-{\frac {1}{2}\sqrt {1-4\,c}};\,1-\sqrt {1-4\,a};\,x)}{\it \_C2}+{x}^{{\frac {1}{2}\sqrt {1-4\,a}}+{\frac {1}{2}}}{\mbox {$_2$F$_1$}(-{\frac {1}{2}\sqrt {1-4\,a-4\,b-4\,c}}+{\frac {1}{2}\sqrt {1-4\,a}}+{\frac {1}{2}}+{\frac {1}{2}\sqrt {1-4\,c}},-{\frac {1}{2}\sqrt {1-4\,a-4\,b-4\,c}}+{\frac {1}{2}\sqrt {1-4\,a}}+{\frac {1}{2}}-{\frac {1}{2}\sqrt {1-4\,c}};\,\sqrt {1-4\,a}+1;\,x)}{\it \_C1} \right ) \right \} \] Mathematica raw input
DSolve[(a + b*x + c*x^2)*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)+(c*x^2+b*x+a)*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = (-1+x)^(-1/2*(1-4*a-4*b-4*c)^(1/2)+1/2)*(x^(-1/2*(1-4*a)^(1/2)+1/2)*hypergeom([-1/2*(1-4*a-4*b-4*c)^(1/2)-1/2*(1-4*a)^(1/2)+1/2+1/2*(1-4*c)^(1/2), -1/2*(1-4*a-4*b-4*c)^(1/2)-1/2*(1-4*a)^(1/2)+1/2-1/2*(1-4*c)^(1/2)],[1-(1-4*a)^(1/2)],x)*_C2+x^(1/2*(1-4*a)^(1/2)+1/2)*hypergeom([-1/2*(1-4*a-4*b-4*c)^(1/2)+1/2*(1-4*a)^(1/2)+1/2+1/2*(1-4*c)^(1/2), -1/2*(1-4*a-4*b-4*c)^(1/2)+1/2*(1-4*a)^(1/2)+1/2-1/2*(1-4*c)^(1/2)],[(1-4*a)^(1/2)+1],x)*_C1)