When you said "Tbh i dont even understand the question" I assumed you simply didn't know where to start on the question altogether. For 9b, as I said, just take your
dxdy=−y(1+ln(x)) and differentiate it again to find
dy2d2x. Then multiply both sides by
y of the expression and tidy it up.
For Q5 if you start your inductive step with
r=1∑k+1[r⋅(21)r]=2−(k+2)(21)k+(k+1)(21)k+1 and up with
2−(k+3)(21)k+1 then you've basically proved it. You can turn it into
2−[(k+1)+2](21)k+1 for clarity which shows that if the statement is true for
n=k then it is true for
n=k+1 and you just need to write an ending statement to that.