For each of the following initial value problems verify that the accompanying functions is a solution. (i) `x(dy)/(dx)=1,\ y(1)=0 => y=logx` (ii) `(dy)/(dx)=y ,\ y(0)=1 => y=e^x` (iii) `(d^2y)/(dx^2)+y=0,\ y(0)=0,\ y^(prime)(0)=1 => y=sinx` (iv) `(d^2y)/(dx^2)-(dy)/(dx)=0,\ y(0)=2,\ y^(prime)(0)=1 => y=e^x+1`