ODE
\[ (a-x) (A+2 x) (b-x) y'(x)+(a-x)^2 (b-x)^2 y''(x)+B y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.270374 (sec), leaf count = 152
\[\left \{\left \{y(x)\to e^{-\frac {(a+A+b) (\log (x-a)-\log (x-b))}{a-b}} \left (c_1 \exp \left (\frac {\left (\sqrt {B} \sqrt {\frac {(a+A+b)^2}{B}-4}+a+A+b\right ) (\log (x-a)-\log (x-b))}{2 (a-b)}\right )+c_2 \exp \left (\frac {\left (-\sqrt {B} \sqrt {\frac {(a+A+b)^2}{B}-4}+a+A+b\right ) (\log (x-a)-\log (x-b))}{2 (a-b)}\right )\right )\right \}\right \}\]
Maple ✓
cpu = 0.46 (sec), leaf count = 170
\[\left [y \left (x \right ) = \textit {\_C1} \left (\frac {a -x}{b -x}\right )^{\frac {\sqrt {A^{2}+\left (2 a +2 b \right ) A +a^{2}+2 a b +b^{2}-4 B}}{2 a -2 b}} \left (\frac {b -x}{a -x}\right )^{\frac {a +b +A}{2 a -2 b}}+\textit {\_C2} \left (\frac {a -x}{b -x}\right )^{-\frac {\sqrt {A^{2}+\left (2 a +2 b \right ) A +a^{2}+2 a b +b^{2}-4 B}}{2 a -2 b}} \left (\frac {b -x}{a -x}\right )^{\frac {a +b +A}{2 a -2 b}}\right ]\] Mathematica raw input
DSolve[B*y[x] + (a - x)*(b - x)*(A + 2*x)*y'[x] + (a - x)^2*(b - x)^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (E^(((a + A + b + Sqrt[-4 + (a + A + b)^2/B]*Sqrt[B])*(Log[-a + x] - Log[-b + x]))/(2*(a - b)))*C[1] + E^(((a + A + b - Sqrt[-4 + (a + A + b)^2/B]*Sqrt[B])*(Log[-a + x] - Log[-b + x]))/(2*(a - b)))*C[2])/E^(((a + A + b)*(Log[-a + x] - Log[-b + x]))/(a - b))}}
Maple raw input
dsolve((a-x)^2*(b-x)^2*diff(diff(y(x),x),x)+(a-x)*(b-x)*(A+2*x)*diff(y(x),x)+B*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*(1/(b-x)*(a-x))^((A^2+(2*a+2*b)*A+a^2+2*a*b+b^2-4*B)^(1/2)/(2*a-2*b))*((b-x)/(a-x))^((a+b+A)/(2*a-2*b))+_C2*(1/(b-x)*(a-x))^(-(A^2+(2*a+2*b)*A+a^2+2*a*b+b^2-4*B)^(1/2)/(2*a-2*b))*((b-x)/(a-x))^((a+b+A)/(2*a-2*b))]