Given $y=sin[ln(1+x)].$

Show that:

$(i),(1+x{)}^2{y}_2+(1+x)y_1+y=0$ where $y_1$ and $y_2$ are

the first and second derivatives respectively.

$(ii),(1+x{)}^2{y}_{n+2}+(2n+1)(1+x)y_{n+1}+(n^2+1)y_n=0.$