\[ y''(x)=-\frac {y'(x) \left ((x-a)^2 (\alpha +\beta +1) (x-b)+(x-a) (-\alpha -\beta +1) (x-b)^2\right )}{(x-a)^2 (x-b)^2}-\frac {\alpha \beta (a-b)^2 y(x)}{(x-a)^2 (x-b)^2} \] ✓ Mathematica : cpu = 0.122026 (sec), leaf count = 50
\[\left \{\left \{y(x)\to c_1 e^{\alpha (\log (x-a)-\log (x-b))}+c_2 e^{\beta (\log (x-a)-\log (x-b))}\right \}\right \}\] ✓ Maple : cpu = 0.224 (sec), leaf count = 39
\[ \left \{ y \left ( x \right ) ={\it \_C1}\, \left ( {\frac {a-x}{b-x}} \right ) ^{\beta }+{\it \_C2}\, \left ( {\frac {a-x}{b-x}} \right ) ^{\alpha } \right \} \]