DSolve[y*(1 - y)*h''[y] + ((a + b) - (1 + a + b)*y) h'[y] - a*b*h[y] == 0, h[y], y]

AsymptoticDSolveValue[y*(1 - y)*h''[y] + ((a + b) - (1 + a + b)*y) h'[y] - a*b*h[y] == 0,

h[y], {y, Infinity, 1}]

AsymptoticDSolveValue[{y*(1 - y)*h''[y] + ((a + b) - (1 + a + b)*y) h'[y] - a*b*h[y] == 0,

 h[1] == 1}, h[y], {y, 1, 1}]