Reduce order and respect a singular boundary

(i) Use $z=(2x-1)dy/dx$ to express $(2x-1)d^2y/dx^2=2(1-dy/dx)$ as an equation in $z,x$.2 marks

(ii) Solve with $y=2$ and $dy/dx=2$ at $x=0$.5 marks

(iii) Describe the gradient as (a) $x\to\pm\infty$ 1 mark and (b) $x\to1/2$.1 mark

(iv) Sketch the solution from (ii).2 marks