\[
\boxed{
{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left( x \right) =-{\frac { \left(  \left( \alpha+\beta+1 \right)  \left( x-a \right) ^{2} \left( x-b \right) + \left( 1-\alpha-\beta \right)  \left( x-b \right) ^{2} \left( x-a \right)  \right) {\frac {\rm d}{{\rm d}x}}y \left( x \right) }{ \left( x-a \right) ^{2} \left( x-b \right) ^{2}}}-{\frac {\alpha\,\beta\, \left( a-b \right) ^{2}y \left( x \right) }{ \left( x-a \right) ^{2} \left( x-b \right) ^{2}}}=0}
\]