DSolve[Derivative[2][y][x] == -((alpha*(a - b)^2*beta*y[x])/((-a + x)^2*(-b + x)^2)) - (((1 + alpha + beta)*(-a + x)^2*(-b + x) + (1 - alpha - beta)*(-a + x)*(-b + x)^2)*Derivative[1][y][x])/((-a + x)^2*(-b + x)^2),y[x],x]