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 = 0.100065 (sec), leaf count = 156
\[\left \{\left \{y(x)\to e^{-\frac {(a+A+b) (\log (x-a)-\log (x-b))}{a-b}} \left (c_1 \exp \left (\frac {\left (\sqrt {B} \sqrt {\frac {(a+A+b)^2-4 B}{B}}+a+A+b\right ) (\log (x-a)-\log (x-b))}{2 (a-b)}\right )+c_2 \exp \left (\frac {\left (-\sqrt {B} \sqrt {\frac {(a+A+b)^2-4 B}{B}}+a+A+b\right ) (\log (x-a)-\log (x-b))}{2 (a-b)}\right )\right )\right \}\right \}\]
Maple ✓
cpu = 0.186 (sec), leaf count = 143
\[ \left \{ y \left ( x \right ) = \left ( {\frac {b-x}{a-x}} \right ) ^{{\frac {b+a+A}{2\,a-2\,b}}} \left ( \left ( {\frac {a-x}{b-x}} \right ) ^{{\frac {1}{2\,a-2\,b}\sqrt {{A}^{2}+ \left ( 2\,a+2\,b \right ) A+{a}^{2}+2\,ab+{b}^{2}-4\,B}}}{\it \_C1}+ \left ( {\frac {a-x}{b-x}} \right ) ^{-{\frac {1}{2\,a-2\,b}\sqrt {{A}^{2}+ \left ( 2\,a+2\,b \right ) A+{a}^{2}+2\,ab+{b}^{2}-4\,B}}}{\it \_C2} \right ) \right \} \] 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[((a + A + b)^2 - 4*B)/B]*Sqrt[B])*(Log[-a + x] - Log[-b + x]))/(2*(a - b)))*C[1] + E^(((a + A + b - Sqrt[((a + A + b)^2 - 4*B)/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),'implicit')
Maple raw output
y(x) = ((b-x)/(a-x))^((b+a+A)/(2*a-2*b))*((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))*_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))*_C2)